Suppose the cost function associated with a product is dollars and the revenue function is , where c denotes the unit cost of production, s denotes the unit selling price, F denotes the fixed cost incurred by the firm, and x denotes the level of production and sales.

Question

Suppose the cost function associated with a product is  dollars and the revenue function is  , where c denotes the unit cost of production, s denotes the unit selling price, F denotes the fixed cost incurred by the firm, and x denotes the level of production and sales. ​

Quizplus · Accepted Answer

The profit function is given by:
P(x) = R(x) - C(x)
where,
R(x) = s*x
C(x) = F + c*x
Thus,
P(x) = sx - F - cx
To obtain the maximum profit, we need to differentiate P(x) w.r.t x and equate it to zero.
dP/dx = s - c = 0
=> s = c
Thus, the maximum profit occurs when the unit selling price is equal to the unit cost of production. 
Substituting s = c in the profit function, we get:
P(x) = (s-c)*x - F
=> P(x) = 0*x - F 
=> P(x) = -F
Thus, the maximum profit is equal to the negative of fixed cost incurred by the firm. 
Hence, option C is the best choice, as it represents the maximum profit.

Suppose the Cost Function Associated with a Product Is