Please show me steps A particular computing company finds that its weekly profit
ID: 2859713 • Letter: P
Question
Please show me steps
A particular computing company finds that its weekly profit, in dollars, from the production and sale of x laptop computers is P(x) = -0.004x^3 - 0.2x^2 + 500x - 700. Currently the company builds and sells 7 laptops weekly. What is the current weekly profit? How much profit would be lost if production and sales dropped to 6 laptops weekly? What is the marginal profit when x = 7? Use the answer from part (a)-(c) to estimate the profit resulting from the production and sale of 8 laptops weekly. The current weekly profit is $ (Round to the nearest cent as needed.) The decrease in profit is $. (Round to the nearest cent as needed.) The marginal profit when x = 7 is $. (Round to the nearest cent as needed.) The profit resulting from the production and sale of 8 laptops weekly is approximately $. (Round to the nearest cent as needed.)Explanation / Answer
a)
P(x) = 0.004*x^3 - 0.2*x^2 + 500x - 700
for x= 7
P(x) = 0.004*x^3 - 0.2*x^2 + 500x - 700
= 0.004*7^3 - 0.2*7^2 + 500*7 - 700
=$2791.6
Answer: $2791.6
b)
for x= 7
P(x) = 0.004*x^3 - 0.2*x^2 + 500x - 700
= 0.004*6^3 - 0.2*6^2 + 500*6 - 700
=$2293.7
Profit lost = $2791.6 - $2293.7 = $496.9
Answer: $496.9
c)
P(x) = 0.004*x^3 - 0.2*x^2 + 500x - 700
dP(x)/dx = 0.004*3*x^2 - 0.2*2*x + 500
for x = 7,
dP/dx = 0.004*3*7^2 - 0.2*2*7 + 500
=497.8
Answer: $497.8
d)
When x = 8
P(8) = p(7) + revenue
= 2791.6 + 497.8
= 3289.4
Answer: $3289.4