Question #205369

Questions 1 and 2 are based on the following information:

The demand and total cost functions for a commodity are

Q = 6 000 − 30P and TC = 5 000 + 2Q,

where P and Q are the price and quantity, respectively.

The total revenue function (TR), in terms of P and the company's quantity, if a commodity sells for R199.00 are?

a. TR = 6 000 − 30P ; Q = 30.

b. TR = 6 000P − 30P ^{2}; Q = 30.

c. TR = P (6 000 − 30P ); Q = 24.

d. TR = 6 000 − 30P ; Q = 24.

What is the company's profit function in terms P?

a. Profit = −30P ^{2} + 6 060P − 17 000

b. Profit = −30P ^{2} + 5 940P − 17 000

c. Profit = −30P ^{2} + 5 940P + 7 000

d. Profit = −30P ^{2} + 6 060P − 7 000

Expert's answer

**1** The total revenue function (TR), in terms of P and the company's quantity, if a commodity sells for R199.00 are?

TR = Q * P = 6 000 P - 30 P^{2}; Q = 6 000 - 30 P = 6 000 - 30 *199 = 30

**Aswer: b**

**2** What is the company's profit function in terms P?

TC = 5 000 + 2 Q = 5 000 + 2(6 000 - 30 P) = 17 000 - 60 P

Profit = TR - TC = 6 000 P - 30 P^{2} - (17 000 - 60 P) = -30 P^{2} + 6 060 P - 17 000

**Aswer: a**

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