Answer:
The correct answer is 38.5
Step-by-step explanation:
Cost function is given by C = 31x + 500
Demand function is given by p = 46 − 0.1 x ,
where p is the price, x is the number of units, and C is the cost.
Revenue function (R) is given by p × x = 46x - 0.1 [tex]x^{2}[/tex]
Profit π = R - C
⇒ π = 46x - 0.1 [tex]x^{2}[/tex] - 31x + 500.
To maximize profit we find [tex]\frac{d}{dx}[/tex]π and equate it to zero.
⇒ 46 - 0.2x -31 = 0
⇒ 15 = 0.2x
⇒ x = 75.
Price at quantity x is equal to 75 = 46 - 7.5 = 38.5
Thus the price at which the profit maximizes for the given demand and price functions is 38.5.
