# Guitars

Suppose the demand for guitars in State College is given by Qd = 5,000 – 5P where Qd is the quantity demanded, and P is the price of guitars. Also, suppose the supply of guitars is given by Qs = 20P – 2000, where Qs is the quantity supplied of guitars.

a) Calculate the equilibrium price of guitars and the equilibrium quantity of guitars in State College. Show your work.

b) Suppose the actual price of guitars is \$300. Determine if there is a shortage, a surplus, or if the market is in equilibrium at a price of \$300. If there is a shortage or surplus, calculate how much the shortage or surplus is.

c) Given your answer to b), is the price of guitars likely to rise, fall, or stay the same?

d) Suppose guitars and guitar strings are complements. On the back, draw a graph indicating what will happen in the market for guitar strings if the price of guitars decreases. Be sure to label your graph carefully, putting Price on the vertical axis and Quantity on the horizontal axis. You do not need to have actual numbers on this graph, but you should clearly indicate how the decrease in the price of guitars will affect the market for guitar strings, and what will happen to the equilibrium price and quantity of guitar strings.

(a) (12, 5) + (6, 3)
(b) (−3, 8) + (6, −2)
(c) (3, 8, −7) + (7, 2, 17)
(d) (a, b, c) + (d, e, f)

Draw each of the following pairs of vectors on a coordinate system, using separate coordinate systems for parts a and b of the question. Then, on each coordinate system, also draw the vectors –B, A + B, and A – B. Label all your vectors.
(a) A = (0, 5); B = (3, 0)
(b) A = (4, 1); B = (2, –3)

The famous Y.S. Chang Restaurant is open 24 hours a day. Waiters report for duty at 3 A.M., 7 A.M., 11 A.M., 3 P.M., 7 P.M., or 11 P.M., and each works an 8-hour shift. Shifts pay different rates. See Table A for the shifts and their rates. Table B shows the minimum number of workers needed during the six periods into which the day is divided. Chang’s scheduling problem is to determine how many waiters should report for work at the start of each time period to minimize the total cost of staff required for one day’s operation. Solve this so that your answers are in the green boxes.

The Battery Park Stable feeds and houses the horses used to pull tourist-filled carriages through the streets of Charleston’s historic waterfront area. The stable owner, an ex-racehorse trainer, recognizes the need to set a nutritional diet for the horses in his care. At the same time, he would like to keep the overall duty cost of feed to a minimum.

The feed mixes available for the horses’ diet are an oat product, a highly enriched grain, and a mineral product. Each of these mixes contains a certain amount of five ingredients needed daily to keep the average horse healthy. The table on this page shows these minimum requirements, units of each ingredient per pound of feed mix, and costs for the three mixes.

In addition, the stable owner is aware that an overfed horse is a sluggish worker. Consequently, he determines that 6 pounds of feed per day are the most that any horse needs to function properly. Formulate this problem and solve for the optimal daily mix of the three feeds that minimizes the total cost of the mix.

Eddie Kelly is running for reelection as mayor of a small town in Alabama. Jessica Martinez, Kelly’s campaign manager during this election, is planning the marketing campaign, and there is some stiff competition. Martinez has selected four ways to advertise: television ads, radio ads, billboards, and newspaper ads. The costs of these and the audience reached by each type of ad is shown in the table below.

In addition, Martinez has decided that there should be at least six ads on TV or radio or some combination of those two. The amount spent on billboards and newspapers together must not exceed the amount spent on TV ads. Each type of ad may not be used more than 10 times. The monthly budget for advertising has been set at \$15,000. How many ads of each type should be placed to maximize the total number of people reached? (Do not round)

Daniel Grady is the financial advisor for a number of professional athletes. An analysis of the long-term goals for many of these athletes has resulted in a recommendation to purchase stocks with some of their income that is set aside for investments. Five stocks have been identified as having very favorable expectations for future performance. Although the expected return is important in these investments, the risk, as measured by the beta of the stock, is also important. (A high value of beta indicates that the stock has a relatively high risk.) The expected return and the betas for five stocks are given below.

Daniel would like to minimize the beta of the stock portfolio (calculated using the sum product of each stock’s beta and the proportion of the investment in that stock). He requires an expected return of at least 11%. In addition, Daniel has decided that no more than 35% of the portfolio should be invested in any one stock.

Determine the proportion of the portfolio that should be in each stock. (For example, if 20% of the portfolio is in stock A, you will get an answer of 0.2). Since you are working with proportions, you will need a constraint that the sum of the proportions is equal to 1.

# Work shown

1. Jacksonville Technical College received \$3,445,553 in state aid on September 15 for the fall academic semester. The vice-president for finance decided to invest \$2,000,000 in a 2-month investment that pays 11.5% simple interest. How much interest will the college earn on the investment? (15 points)

2. Barney Casey borrowed \$40,000 from his parents for 2 years. He paid them a total of \$45,000 at the end of the 2-year term of the simple interest loan. What rate of interest did he pay his parents? (15 points)

3. Sarai Sherman agreed to deposit \$4,450 in an account paying 16% simple interest per year for 60 days. If she made the deposit on February 25, determine (a) the date of the end of the term of the investment, and (b) the ordinary interest Sarai will earn. (15 points)

4. Anna Cavanaugh loaned her friend Jason \$1,000 for 6 months at 6% simple interest. What is the future value of the loan and how much finance charge will Jason pay? (15 points)

5. Acton can choose from two loan offers: \$12,000 at 8% simple interest for 9 months; or a \$12,000 9-month discounted loan at 7% discount. Based on the actual interest paid and the true rate on the discounted loan, which of the two loan offers will Acton choose? Explain your answer. (40 points)

6. Envision that you have served as business manager of Media World for over 2 years. You have noticed that for the last 12 months the business has regularly had cash assets of \$20,000 or more at the end of each month. You have found a 6-month certificate of deposit that pays 6% compounded monthly. To obtain this rate of interest, you must invest a minimum of \$2,000. You have also found a high interest savings account that pays 3% compounded daily. Based on the cash position of the business at this time, assume that you decide to invest \$4,000.

1. Assume that you will invest the full amount in a certificate of deposit.

a. What would be the future value of the CD at the end of the investment term? (14 points)
b. How much interest would the investment earn for the period? (14 points)
c. What would be the effective rate of the investment?(14 points)

2. Assume that you decide to invest the \$4,000 in the high-interest savings account.

a. What future value would you expect to receive at the end of 6 months? (14 points)
b. How much interest would the investment earn for the period? (14 points)
c. What would be the effective rate of the investment? (14 points)

3. Write a recommendation to the partners justifying a short-term investment of business funds at this time, recommending one of these investments. Include your analysis from questions 1 and 2 in your recommendation