1. For most products, higher prices result in a decreased demand, whereas lower prices result in an increased demand. Let

d = annual demand for a product in units p = price per unit

Assume that firm accepts the following price-demand relationship as being realistic: d = 800 – 10p where p must be between $ 20 and $70. a. How many units can the firm sell at the $ 20 per-unit price? At the $ 70 per-unit price? b. Show the mathematical model for the total revenue (TR), which is the annual demand multiplied by the unit price. c. Based on other considerations, the firm’s management will only consider price alternative that will maximize the

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TC = 80 000 + 3x

TR = 20 x TP= TR – TC = 17 x – 80 000

a) break-even point TP = 0 => x = 4706 copies

b) TP (4 000) = -12 000 (loss = 12 000)

c) If x = 4 000 is break even , publisher needs price p satisfying equation

TC (4 000) = TR (4 000)

or

80 000 + 3* 4 000 = p* 4 000

80. 000 = (p – 3) 4 000

p – 3 = 20 => p =23

d) For p = 25.95 TR = 25.95x

TP = TR – TC =22.95 x – 80 000

If x = 4 000, publisher has positive profit TP(4 000) = 91 800 – 80 000 = 11 800

5. Preliminary plans are underway for the construction of new stadium for a major league baseball team. City officials question the number and profitability of the luxury corporate boxes planned for the upper deck of the stadium. Corporations are selected individuals may buy the boxes for $ 100,000 each. The fixed construction cost for the upper-deck area is estimated to be $ 1,500,000 with a variable cost of $50,000 for each box constructed. a. What is the breakeven point for the number of luxury boxes in the new stadium? b. Preliminary drawings for the stadium show that space is available and that all 50 could be sold if constructed. What is your recommendation concerning the construction of luxury boxes?