statistics

Joanne sells silk-screened T-shirts at community festivals and craft fairs. Her marginal cost to produce one T-shirt i $4.50. Her total cost to produce 40 T-shirts is $230, and she sells them for $8 each. a. Find the linear cost function for Joanne's T-shirt production. b. How many T-shirts must she produce and sell in order to break even? c. How many T-shirts must she produce and sell to make a profit of $700? A firm produces a product that has the production cost function C(x) = 270x + 13,410 and the revenue function R(x) =360x. No more than 42 units can be sold. Find and analyze the break-even quantity, then find the profit function. A person is the manager of a firm. He is considering manufacturing a new product, so he asks the accounting department for cost estimates and the sales department for sales estimates. After he receives the data, he must decide whether to go ahead with production of the new product. Analyze the following data (find a break-even quantity) and then decide what the manager would do in this case. Also, write the profit function. C(x) =120x + 600 and R(x) = 105x D The Consumer Price Index (CPI) is a measure of the change in the cost of goods over time. The index was 100 for the three-year period centered on 1983. For simplicity, we will assume that the CPI was exactly 100 in 1982. Then the CPI of 205.6 in 2006 indicates that an item that cost $1.00 in 1982 would cost $2.06 in 2006. The CPI has been increasing approximately linearly over the last few decades. a. Use this information to determine an equation for the CPI in terms of t, which represents the years since 1982. b. Based on the answer to part (a), what was the predicted value of the CPI in 2000? Compare this estimate with the actual CPI of 177.8. c. Describe the rate at which the annual CPI is changing. A company is upgrading office technology by purchasing inkjet printers, LCD monitors, and additional memory chips. n The total number of pieces of hardware purchased is 43. The cost of each inkjet printer is $117, the cost of each LCD monitor is $139, and the cost of each memory chip is $80. The total amount of money spent on new hardware came to $4459. They purchased two times as many memory chips as they did LCD monitors. Determine the number of each that was purchased. F Ana invests $26,000 received from her grandmother in three ways. With one part, she buys savings bonds at an interest rate of 1.5% per year. She uses the second part, which amounts to 6 times the first, to buy mutual funds that offer a return of 7% per year. She puts the rest of the money into a money market account paying 5.5% annual interest. The first year, her investments bring a return of $1530. How much did she invest each way? (Hint: For 1.5% interest, the amount of interest paid on x dollars is 0.015x.)