A company decides to begin making and selling computers. The price function Is g

Question

A company decides to begin making and selling computers. The price function Is given as follows: p = -65x + 1300, where x is the number of computers that can be sold at a price of p dollars per unit. Additionally, the financial department has determined that the weekly fixed cost of production will be 5000 dollars with an additional cost of 250 dollars per unit. (A) Find the revenue function in terms of x. R(x) = (B) Use the financial department's estimates to determine the cost function in terms of x. C(x) = (C) Find the profit function in terms of x. P(x)= -65x+1300 (D) Evaluate the marginal profit at x = 250· P(250) =

Explanation / Answer

A)

we have to find the revenue in terms of x.

we know that revenue is given by R = price * number of units = p*x

as given we have price function p = -65x + 1300

so we can say that revenue R(x) = (-65x+1300)x = -65x2 + 1300x

B)

we have to use financial deparment's estimates to determine cost function in terms of x

we know that cost = fixed cost + variable cost

as given weekly fixed cost pf production will be 5000 dollars with additional cost of 250 dollars per unit

so C(x) = 5000 + 250x

c)

we have to find the profit function in terms of x

we know that profit = revenue - cost

P(x) = R(x) - C(x)

P(x) = -65x2 + 1300x - 5000 - 250x

P(x) = -65x2 + 1050x - 5000

D)

we have to find the marginal profit at x = 250

we have P(x) = -65x2 + 1050x - 5000

so P'(x) = d/dx(-65x2 + 1050x - 5000)

P'(x) = -130x + 1050

put x = 250 we have,

P'(250) = -130*250 + 1050 = -32500 + 1050 = $31450

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.