Problem: Looking for the production level that maximizes profit
A company manufactures and sells x pocket calculators per week. If weekly cost and demands equations are given by:
C(x)= 8,000+5x p=14-(x/4,000) 0`<=`x`<=` 25000
The cost equation for the pocket calculators is C(x) = 8000 + 5x. The demand equation is p = 14 - x/4000.
If x calculators are sold, the revenue is p*x = 14x - x^2/4000. The cost of producing x calculators is 8000 + 5x. This gives the profit earned as: P(x) = 14x - x^2/4000 - 8000 - 5x
To determine the value of x that maximizes profit, solve P'(x) = 0
=> 9 - (2x)/4000 = 0
=> x = 9*2000 = 18000
The weekly production of calculators should be 18000 to maximize profit.