A group of college students are starting a small business called Custom Tech. They make customized cell phone and tablet cases. Their profits are $40 for the cell phone case and $60 for the tablet case. The process involves both design hours and manufacturing hours. It takes 0.5 hour to design and 0.3 hour to manufacture a customized phone case. It takes 0.4 hour to design and 0.4 hour to manufacture a customized tablet case. Since the design part is completed by students attending school, they can allocate no more than 100 hours per day for design. They are sharing a single manufacturing machine with another company and only have 8 hours per day to use it. Let x represent the number of customized cell phone cases and y represent the number of customized tablet cases. a. Write the profit objective function. b. Write the design constraint inequality. c. Write the manufacturing constraint inequality. d. Graph the constraint inequalities. Identify the coordinates of the feasible region. How many of each type of customized case must they sell to maximize their profits? Constraints
> How much more would $10,000 earn in 3 years compounded daily at 1.33%, than compounded semi-annually at 4.33%? Round to the nearest cent.
> Nick deposited $3,000 in a 3-year CD account that pays 4.08% interest, compounded weekly. What is the ending balance? Round to the nearest cent.
> Matt has two single accounts at Midtown Bank. One account has a balance of $74,112.09 and the other has a balance of $77,239.01. a. What is the sum of Matt’s balances? b. Is all of Matt’s money insured by the FDIC? Explain.
> Nine months ago Alexa deposited $7,000 in a 3-year CD. She has received $224.16 in interest. She withdraws $1,000. This is before the CD matures, so she pays a $250 penalty. What is her balance after the withdrawal?
> Ruth has a savings account at a bank that charges a $3.50 fee for every month her balance falls below $1,500. Her account has $1,722 and then she withdraws $400. What is her balance in 5 months if her account balance never reaches $1,500? Round to the ne
> How might those words apply to what you have learned in this lesson?
> Find the simple interest on a $2,219.00 principal, deposited for 6 years at a rate of 1.91%. Round to the nearest cent.
> Rebecca opened a savings account on March 20 with a $5,200 deposit. The account pays 3.99% interest, compounded daily. On March 21 she made a $700 deposit, and on March 22 she made a $500 withdrawal. Use this information to find the missing amounts. Roun
> Rhonda deposits $5,600 in a savings account that pays 1½% interest, compounded semi-annually. Round to the nearest cent. a. How much interest does the account earn in the first 6 months? b. What is the ending balance after 6 months? c. How much intere
> Jean owned x shares of a corporation and received a quarterly dividend check for y dollars. Express the annual dividend for one share algebraically.
> Ralph deposited $910 in an account that pays 1.75% simple interest for 3 years. Round to the nearest cent. a. How much interest did the account earn? b. What is the ending balance? c. How much interest did the account earn the first year? d. How much
> Use the check register from Exercise 1. It is now 1 month later, and the checking account statement has arrived. Does the account balance? Checking Account Statement Exercise 1: Go to www.cengage.com/financial_alg2e and download a blank check registe
> Go to www.cengage.com/financial_alg2e and download a blank check register. Add all of the following information to the check register. a. The balance on December 10 is $3,900.50. b. On December 11 check 1223 is written for $84.00 to the North Shore Hig
> Use the credit card statement and a blank credit card calendar. a. What is the total of all of the purchases made this billing cycle? b. What is the amount of total payments? c. What is sum of the daily balances? d. What is the average daily balance
> Kayla wants to take out a $7,500 loan with a 3.3% APR. She can afford to pay $128 per month for loan payments. a. What should be the length of her loan? Round to the nearest tenth of a year. b. What would an increase of $20 to the monthly payment do to
> Bill can afford a monthly payment of $475. He wants to take out a $20,000 loan at a 4.25% interest rate. What should the length of the loan be? Round your answer to the nearest year.
> The table lists the balances at the end of each year for a 15-year, $50,000 loan with an 8% interest rate. Year ………………………………………………………………………………………………. Balance 0 ………………………………………………………………………………………………. $50,000.00 1 ………………………………………………………………………………………………. $48,
> Irina’s credit card has an APR of 16.8%. She never pays her balance in full, so she always pays a finance charge. Her next billing cycle starts today. The billing period is 30 days. Today’s balance is $712.04. She is only going to use the credit card onc
> Examine the summary section of the monthly credit card statement. Use the first five entries to determine the new balance. Finance Charge New Balance Minimum Рayment Previous Payments / Credits New Late SUMMARY Balance Purchases Charge $421.36 $1,70
> Harold borrowed $8,000 for 5 years at an APR of 2.75%. a. What is Harold’s monthly payment? Round to the nearest cent. b. What is the total amount that Harold paid in monthly payments for the loan? c. What is the amount Harold will pay in finance char
> Mike owned 3,000 shares of CreeChurrs Corporation and received a quarterly dividend check for $1,140. What was the annual dividend for one share of CreeChurrs?
> What is the monthly periodic rate on a loan with an APR of 19.5%?
> Riel had an average daily balance of $415.22 on his May credit card statement. The bill showed that his APR was 21.6% and that his finance charge was $89.69. When he verified the finance charge, did he find that it was correct or incorrect? Explain.
> The finance charge on Lena’s credit card bill last month was $13.50. Her APR is 18%. What was her average daily balance?
> Michelle’s credit card billing cycle is 30 days. She had a daily balance of b dollars for d days. Then she charged one item for $56, and she made no more purchases for the rest of the month. There was no other activity on the credit card. Express her ave
> Kim’s credit card was not paid in full last month so she will pay a finance charge this month. She had an average daily balance of d dollars during this billing period, which had 31 days. The APR was p percent. a. Express the APR as an equivalent decima
> Blair had these daily balances on his credit card for his last billing period. He did not pay the card in full the previous month, so he will have to pay a finance charge. The APR is 18.6%. 2 days @ $331.98 11 days @ $1,203.04 4 days @ $996.71 13 day
> Juan purchased a tool set for t dollars on the installment plan. He made a 15% down payment and agreed to pay m dollars per month for the next y years. Express the finance charge algebraically.
> Ben has been accepted into a 2-year culinary arts program at the Greenfield Career Institute. He has been approved for a $5,000 unsubsidized 10-year federal loan at 4.29%. He knows he has the option of beginning repayment of the loan in 2.5 years. He als
> Laura deposits $10,000 into an account that compounds interest continuously at a rate of 2.2%. To the nearest tenth of a year, how long will it take her money to grow to $10,800?
> How might the quote by Baldwin apply to what you have learned in this section?
> A minivan is traveling at 80.5 kilometers per hour. Cargo is strapped to the roof at a height of 1.75 meters. The car hits a concrete barrier, and the cargo is ejected from the roof. Use the following two equations to determine how long it takes for the
> Cargo is tied with rope on the roof of a 4.5-foot-tall car. The car travels down a road at 40 mi/h and hits a concrete barrier and the rope snaps, allowing the cargo to propel forward. Find the time it takes for the cargo to hit the ground and the horizo
> Ghada works for an insurance company as an accident reconstruction expert. She measured a 52-ft chord from the outer rim of the yaw mark on the road surface. The middle ordinate measured x ft in length. The drag factor of the road surface was determined
> Talia bought a $5,000 Pelts Corp bond. The bond pays 5.95% annual interest. How much will Talia receive in interest if she holds the bond for 11 years?
> Express the average daily balance algebraically given this set of daily balances. x days @ y dollars w days @ d dollars r days @ q dollars m days @ p dollars
> Stock in the Happy’s Burger chain was selling for $54.24 per share, and it was paying a $2.46 annual dividend. It underwent a 3-for-1 split. a. What was the new price of one share after the split? b. If you owned 200 shares before the split, how many s
> Sascha owns stock in Lewis Corp, and she bought a $1,000 corporate bond. The bond pays 6.34% annual interest. a. How much will Sascha receive in annual interest? b. How much will Sascha receive in interest if she holds the bond for 14 years? c. Sascha
> The Zeescore Corporation pays an annual dividend of $2 per share. On Wednesday it closed at $61 per share with a net change of 20.85. The dividend remained at $2 for a year. a. What was the yield on Wednesday? Round to the nearest tenth of a percent. b
> Revreg Corp pays an annual dividend of $1.60 per share. On Friday it closed at $44 per share with a net change of 10.35. The dividend did not change. a. What was the yield on Friday? Round to the nearest tenth of a percent. b. At what price did Revreg
> Determine the values of a, b, and c in the following matrix equation. 3 4 а 2 b 5 с 1 8 2 34 4 30 52 ||
> A share of Southside stock sold for $37. The annual dividend is $1.85. Three years later the stock has increased 17% in value and the dividend has increased 5%. a. What is the price per share 3 years later? b. What is the dividend 3 years later? Round
> A political polling company has been assigned to survey local voters a week before the upcoming election. The company will need to hire interviewers and statisticians for the job. Statisticians make $1,200 per week and interviewers make $800 per week. Th
> Greenfield Industries produces rotors for manufacturers in Hartford, Connecticut, and Des Moines, Iowa. Hartford needs at least 21 rotors, and Des Moines needs at least 40 rotors. Greenfield is able to produce and send at most 150 rotors to these two man
> Hi End Rugs manufactures silk and wool fiber rugs. Their warehouse has 2,400 lots of silk fiber and 1,800 lots of wool fiber available during the week of May 5 for production of their Premier and Elegant lines of carpets. A roll of Premier uses 40 lots o
> A financial manager wants to invest up to $400,000 of his client’s money in two investment plans. Plan A pays an annual interest rate of 6% and Plan B pays an annual interest rate of 8%. Although Plan B pays a higher interest rate, there is some risk inv
> Maribel was approved for a 7-year private student loan at 6.8% to cover her college costs of $10,900. a. Determine her monthly payment. Round to the nearest cent. b. What is the total amount she will pay back? c. What is the total interest amount?
> The quarterly dividend for Tiffany, a jewelry company, was $0.40 during the first quarter of 2016. What was the annual dividend for 2,000 shares at that time?
> Van Siclen Farms plants only corn and soybeans on their 4,000-acre fields. The corn yields a profit of $160 per acre, and the soybean profit is $340 per acre. This year the owners have decided to plant no more than 2,400 acres of corn and no more than 3,
> In each of the following, you are given an objective function and the vertices of a feasible region. Determine both the maximum and minimum values of the objective function as well as the point at which they occur. a. P = 11x + 15y (5, 9), (15, 15), (17
> The vertices of a feasible region are listed below. What is the minimum cost for the objective function C = 45x + 53y? a. (3, 7), (15, 20), (22, 20), (23, 5) b. (0, 9), (12, 8), (20, 9), (9, 0)
> The vertices of a feasible region are listed below. What is the maximum profit for the objective function / a. (0, 10), (0, 0), (20, 0) b. (1, 8), (2, 1), (8, 4), (10, 6)
> Use Nate’s matrix N from exercise 7b above. Nate knows that in the spring semester his tuition will increase by 5%, his supplies will decrease by 5%, his transportation will remain the same, his textbook costs will remain the same, and his fees will incr
> Determine whether each of the following points falls within the profit feasible region defined by / a. (0, 5) b. (2, 3) c. (0, 0) d. / e. (1.75, 2.75)
> How might the quote apply to what you have learned in this section?
> Maria purchased 1,000 shares of stock for $35.50 per share in 2014. She sold them in 2016 for $55.10 per share. Express her capital gain as a percent, rounded to the nearest tenth of a percent.
> Elliott purchased shares of Microsoft in 2016 for $52.50 per share. He plans to sell them as soon as the price rises 20%. At what price will he sell his shares?
> Rodrigo is attending a 4-year college. As a freshman, he was approved for a 10-year, federal unsubsidized student loan in the amount of $5,300 at 4.29%. He knows he has the option of beginning repayment of the loan in 4.5 years. He also knows that during
> General Motors stock fell from $41 per share in 2013 to $24.98 per share during 2016. a. If you bought and then sold 300 shares at these prices, what was your loss? b. Express your loss as a percent of the purchase price. Round to the nearest tenth of
> In 2010, Joe bought 200 shares in Nikon Corp for $22.07 per share. In 2016 he sold the shares for $15.11 each. a. What was Joe’s capital loss? b. Express Joe’s capital loss as a percent, rounded to the nearest percent.
> Ramon bought x shares of Xerox stock for a total of $40,000. Express the price he paid per share algebraically.
> Tori bought x shares of Mattel stock for m dollars per share. She sold all of the shares months later for y dollars per share. Express her capital gain or loss algebraically.
> Mitchell bought 600 shares of Centerco 2 years ago for $34.50 per share. He sold them yesterday for $38.64 per share. a. What was the percent increase in the price per share? Round to the nearesttenth of a percent. b. What was the total purchase price f
> Zach bought 200 shares of Goshen stock years ago for $21.35 per share. He sold all 200 shares today for $43 per share. What was his gross capital gain?
> Jess and Nate are married teachers. They keep individual budget charts of their graduate school education–related expenses for tax purposes. The charts below are for the fall semester. a. Let matrix J be a 5 × 4 matrix co
> Jake bought d shares of stock for x dollars per share years ago. His stock rose in price and eventually hit a price that would earn him a 140% capital gain. He decided to sell half of his d shares. a. Represent half of the d shares algebraically. b. Re
> Zeke bought g shares of stock for w dollars per share. His broker called him and told him to sell the shares when they earn a 40% capital gain. a. Express the total purchase price of all the shares algebraically. b. Express the capital gain algebraical
> The policy of the Black Oyster Pawnshop is to lend up to 30% of the value of a borrower’s collateral. Pete wants to use a $2,000 guitar and a $900 camera as collateral for a loan. What is the maximum amount that he could borrow from Black Oyster?
> During 2003, a share of stock in Coca-Cola Co sold for $39. Michelle bought 300 shares. During 2008, the price hit $56 per share, but she decided to keep them. By 2016, the price of a share had fallen to $44, and she had to sell them because she needed m
> Austin purchased shares of stock for x dollars in 2015. He sold them years later for y dollars per share. a. Express his capital gain algebraically. b. Express his capital gain as a percent of the purchase price.
> Is it always true that someone sells a stock because they think it is going to go down in price? How do those words apply to what you’ve learned in this section?
> Helene and Vick moved into an apartment and pay $1,875 rent per month. The landlord told them that the rent has increased 3.28% per year on average. Express the rent y as an exponential function of the number of years they rent the apartment.
> The Basil family has a summer co-op apartment on a beach and pays a monthly mortgage payment of $1,120 and a monthly maintenance fee of $800. The Basils get approval from the co-op board of directors to sublet their apartment, since they do not plan to u
> Linda wants to purchase a Leisure Heights condominium. She will borrow $100,000 from the Duchess Savings Bank. The bank is presently offering a 30-year fixed-rate mortgage with an APR of 4.1%. Her monthly maintenance fee will be $310. a. What is the mon
> Ethel rented an apartment from a landlord in Sullivan County. Her rent was $1,200 per month until she moved out last week. The new tenants pay $1,350 per month. Represent the rent increase as a percent, to the nearest tenth of a percent.
> Raymond pays $1,000 per month in rent, and he is expecting a rent increase. His landlord agreed to a gradual increase according to the following plan: January, 0% increase February, 5% increase March, 10% increase from January April, 15% increase from Ja
> The Jacobs Family owned a condo in Bethpage Acres. They bought it for $130,000 6 years ago and sold it last week for $195,000. Who keeps the profit from the sale?
> Ron has a co-op in Astor Cooperative. The total shares in the cooperative are 40,000 shares. If Ron owns 500 shares, what percentage of the cooperative corporation does he own?
> Sarah is taking out a $24,400, 4-year new-car loan with an APR of 2.88%. What is the finance charge for this loan? Round to the nearest hundred dollars.
> Last year, Anna paid x dollars per month for a co-op maintenance fee. One third of this fee was for property taxes. How much property tax did Anna pay last year?
> Three years ago, Jerry purchased a co-op. This year his monthly maintenance fee is $1,397. Twenty percent of this fee is for Jerry’s property taxes. How much will Jerry pay this year in property taxes?
> Joe wants to rent an apartment with an initial monthly rent of $1,400. He has been told that the landlord raises the rent 1.25% each year. Set up an exponential function that models this situation. Calculate the rent after 12 years. Round to the nearest
> The Tensers bought a mobile home for $89,500. They rent space in a trailer park for $900 per month. The rent increases 2% per year. a. If they put a down payment of $10,000 on the trailer, how much must they borrow? b. If they borrow the amount from pa
> The monthly rent for a one-bedroom apartment at North Shore Towers for 6 consecutive years is shown in the table. Year ……………………………………………………………………………. Monthly Rent ($) 2011 ……………………………………………………………………………………………… 2,500 2012 ………………………………………………………………………………………
> Monthly rent at Countryside Co-ops has increased annually, modeled by the exponential equation y = 2,155(1.062)x-1 . What was the percent increase per year?
> Maria borrowed $120,000 from a bank when she bought her co-op for $156,000. The price dropped x dollars since she bought it. She now owes the bank $114,000, which is more than she could sell the co-op for. Write an inequality that expresses the fact that
> Andrew and Meghan moved into an apartment in the city and pay $2,700 rent per month. The landlord told them the rent has increased 11.1% per year on average. a. Express the rent y as an exponential function of x, the number of years they rent the apartm
> Which of the following matrix operations are defined? 7 8 2 1 0 2 3 6 5 9 9 8 7 C = Given A = 4 B = 6. D = 1 2 3 4 3 4 5 6 2 1 7 8 9 9 4 5 6 E = 8 7 6 5 F = [4 3] G= 0 1 H= 7 8 9 2 3 а. А + В b. А +H с. 2Н — ЗА d. G +H е. ВС f. АЕ g. A? h. D?
> What does this quote mean to you when viewed in the context of what you learned in this section?
> Carly took a $7,000, 3-year loan with an APR of 3.15%. a. What is the monthly payment? Round to the nearest cent. b. What is the total amount of the monthly payments? c. What is the finance charge?
> The historical prices of a car are recorded for 11 years as shown. a. Construct a scatter plot for the data. b. Determine the exponential depreciation equation that models this data. Round to the nearest hundredth. c. Determine the depreciation rate
> A graphing calculator has determined this exponential regression equation based on car value data: y = a∗ bx, a = 18,547.23 5, and b = 0.86255. What is the rate of depreciation for this car? How much is this car worth after 6 years; 78 months; w months?
> A graphing calculator has determined this exponential regression equation based on car value data: y = a∗ bx 5, a = 20,952.11, and b = 0.785 5. What is the rate of depreciation for this car? How much is this car worth after 6 years; 78 months; w years?
> Luisa purchased a used car for D dollars. The car depreciates exponentially at a rate of E% per year. Write an expression for the value of the car in 5 years, in A years, and in M months.
> Laura’s new car cost her $21,000. She was told that this make and model depreciates exponentially at a rate of 8% 5 8 per year. How much will her car be worth after 100 months?
> Chris purchased a used car for $19,700. The car depreciates exponentially by 10% per year. How much will the car be worth after 6 years? Round your answer to the nearest penny.
> Shannon’s new car sold for $28,000. Her online research indicates that the car will depreciate exponentially at a rate of 5.25% per year. Write the exponential depreciation formula for Shannon’s car.
> Seamus bought a car that originally sold for $40,000. It exponentially depreciates at a rate of 7.75% per year. Write the exponential depreciation equation for this car.
> Amber bought a used car valued at $16,000. When this car was new, it was sold for $28,000. If the car depreciates exponentially at a rate of 9% per year, approximately how old is the car?
> What are the dimensions of each of the following matrices? a. [7] -3 b. 3 c. [4 10 17 15 11] с. 1 0 0 d. 0 1 0 0 1 е. 0.5 0.75 0.125 0.2 0 0 0 0
