Write a Quantitative Analysis report on the following problems:

1. The manufacturer of high-quality flatbed scanners is trying to decide what price to set for its product. The costs of production and the demand for product are assumed to be as follows:

TC = 500,000 + 0.85Q + 0.015 Q2

Q = 14,166 - 16.6P

a). Determine the short-run profit-maximizing price.

b). Plot this information on a graph showing AC, AVC, MC, P, and MR.

2.

Price $ Quantity

Adults Children

5 15 20

6 14 18

7 13 16

8 12 14

9 11 12

10 10 10

11 9 8

12 8 6

13 7 4

14 6 2

The marginal operating cost of each unit of quantity is $5. (Hint: Because marginal cost is a constant, so is average variable cost, Ignore fixed cost.). The owners of the amusement park want to maximize profits.

1. Calculate the price, quantity, and profit if

a. The amusement park charges a different price in each market

b. The amusement park charges the same price in the two markets combined.

c. Explain the difference in the profit realized under the two situations.

2.(Mathematical solution) The demand schedules presented in Problem 2 can be expressed in equation form as follows (where subscript A refers to the adult market, subscript C to the market for children, and subscript T to the markets combined)

QA = 20 - PA

QC = 30 - 2PC

QT = 50 - 3PT

Solve these equations for the maximum profit that the amusement park will attain when it charges different prices in the two markets and when it charges a single price for the combined market.