The cost, in thousand of dollars, of making x items, in hundreds, is given by C(x) = −12x − 75. The revenue function is given by R(x) = −6x^2 + 30.

Question

Determine the number of items that should be sold to maximize profit.

Answer 1

R = -6x^2 + 30 is a very strange revenue function. You get 30 by selling nothing, and revenue goes down if you sell anything

C= -12x -75 is a very strange cost function. Costs are negative and get even more negative if you manufacture anything. Fixed "costs" are negative 75

but using these numbers means

profit =R - C = -6x^2 +12x +105

usual method would be

take the derivative and set = zero

where MR = MC, Marginal Revenue = Marginal Cost

derivative = -12x +12 = 0

x = 1

manufacture and sell 1 hundred units gives

"profit" =-6+12+105= 111 thousand dollars

profit maximizing output level is one hundred units

with output more or less than one hundred, profit goes down