Answer to Question #205372 in Math for Akhona Klanisi

Question

7

A firm's total cost function is given     TC = 4 + 8Q − Q²                                

, and total revenue asTR = 50Q − 4Q²,

where Q is the number of units produced and sold (in thousands). How many units should be produced to maximize profit?

 

a.        14

b.        252

c.        7 000

d.        115 904

 

 

Answer 1

7 A firm's total cost function is given TC = 4 + 8Q − Q², and total revenue asTR = 50Q − 4Q²,

where Q is the number of units produced and sold (in thousands). How many units should be produced to maximize profit?

Profit = TR - TC = 50Q - 4Q² - (4 + 8Q - Q²) = 50Q - 4Q² - 4 - 8Q + Q² = -4 + 42Q - 3Q²

Profit has maximum than $\frac{d Profit}{d Q} = 42 - 3*2*Q = 0$ from here Q = 7 (thousands)

Answer: c