formula p=-2x^2+8x+2, where x is the number of units produced per week, in thousands. How many units should the company produce per week to earn the maximum profit? and find the maximum weekly profit.
a. 4,000 units, $300
b. 2,000 units, $1000
c. 4,000 units, $200
d. 2,000 units, $200

Question

formula p=-2x^2+8x+2, where x is the number of units produced per week, in thousands. How many units should the company produce per week to earn the maximum profit? and find the maximum weekly profit. 
a. 4,000 units, $300
b. 2,000 units, $1000
c. 4,000 units, $200
d. 2,000 units, $200

valpey · Answer

The formula for p describes a Concave parabola, so we should expect it to have a maximum profit for some value x. Calculus can help because p' will be zero at the value for x where profit is maximized.

valpey · Answer

$$p(x)=-2x^2+8x+2$$
$$p'(x)=-4x+8$$
Remember x is in 1000's. What is the value of x which gives p'(x) = 0?

anonymous · Answer

well that helps...thanks!

valpey · Answer

Is p in $100's of dollars?