Question

Find the profit in dollars from the sale of x expensive watches is P(x)=0.07x^2 – 4x + 5x^0.8 – 5100. Find the marginal profit when (a) x=400 (b) x=1000 (c) x=6000, and (d) x=12,000.

Answer 1

Answer:

The answers to the question are;

The marginal profit with the respective value of x are given as;

(a)  x=400, P(x)= 10203.42

(b)  x=1000, P(x)= 67255.94

(c) x=6000, P(x)= 25181266.12

(d) x=12,000, P(x)= 10041168.853.

Step-by-step explanation:

To solve the question, we note that the function for profit is given by

P(x) = 0.07·x² - 4·x + 5·$x^{0.8}$

to solve for P(x) when

(a) x=400 we have

P(400) = 0.07·400² - 4·400 + 5·$400^{0.8}$ = 10203.42

The marginal profit when x=400 is 10203.42

(b) x=1000 we have

P(1000) = 0.07·1000² - 4·1000 + 5·$1000^{0.8}$ = 67255.94

The marginal profit when x=1000 is 67255.94

(c) x=6000 we have

P(1000) = 0.07·6000² - 4·6000 + 5·$6000^{0.8}$ = 25181266.12

The marginal profit when x=6000 is 25181266.12

(d) x=12,000.  we have

P(12,000) = 0.07·12,000² - 4·12,000 + 5·$12000^{0.8}$ = 10041168.853

The marginal profit when x = 12,000 is 10041168.853.