Another company sells wrought iron umbrella trees. This company has fixed costs of $100,000/month. The cost in labor and material is $15 per umbrella sold per month. To sell x items, the price must be set at $50-0.5x, where x is in thousands of umbrellas sold per month. What price will maximize profit?
2007-07-02 17:12:48 · 2 answers · asked by ? 1 in Science & Mathematics ➔ Mathematics
profit (P) = income (I) - cost (C)
P = (50-0.5x)x - (100,000 + 15x)
P' = 50 - x - 15
Solve P' = 0 for x,
x = 35
Price = 50-0.5*35 = $32.5
2007-07-02 17:29:53 · answer #1 · answered by sahsjing 7 · 0⤊ 0⤋
Costs are: 100000+15X, where X is umbrellas.
Sales are: X(50-0.5*X/1000)
Profit is: 50X - 0.0005 * X^2 - 100000-15 X
-0.0005*X^2 + 35 X - 100000.
Now take the derivitive of this,, set it equal to zero and determine X. Then determine the price at this value of X.
2007-07-03 00:26:32 · answer #2 · answered by cattbarf 7 · 0⤊ 0⤋