# 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 ...

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

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### 1 Answer

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.**