Calculus problem:?

0 ⤊

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 $50-0.3x, where x is in thousands of umbrellas sold per month. What price will maximize profit?
price=_______________

2007-06-29 15:09:23 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics

2 answers

price = $32.50

2007-06-29 16:51:06 · answer #1 · answered by davec996 4 · 0⤊ 0⤋

Cost = 100,000 +15x
Revenue = (50- .3x)x
Profit = (50-.3x)x - 100000+15x
P = 50x-.3x^2 -100000+15x
P = -.3x^2 +50x -100000
dP/dx = -.6x +50
.6x+ 50
x = 50/.6 = 83.3
Price = 50- 83.33*.3 = 25$

2007-06-30 01:19:37 · answer #2 · answered by ironduke8159 7 · 0⤊ 0⤋