Afirm has monthly average costs, in dollars, given by c = 43,000 x + 200 + x where x is the number of units produced per month. the firm can sell its product in a competitive market for $1800 per unit. if production is limited to 200 units per month, find the number of units that gives maximum profit.

x = 800

but the production of units is limited to 200 units hence profit is not possible with given constraint

Explanation:

Given data:

average cost is = 43000/x + 200 + x, here x denote number of unit

cost of per unit =$1800

total unit produced in one month is 200

Profit can be calculated as

Profit = revenue - cost

P = 1800 - (43000/X + 200 + X)

P X= 1800 X - 43000 - 200X - X^2

PX = - X^2 +  1600 X - 43000

P'X = -2X + 1600X

P'X = 0

x = 800

but the production of units is limited to 200 units hence profit is not possible with given constraint