Suppose a company has fixed costs of $36, 400 and variable costs of 1/3x + 444 d

Question

Suppose a company has fixed costs of $36, 400 and variable costs of 1/3x + 444 dollars per unit here x is the total number of units produced. Suppose further that the selling price of its product is 1772 - 2/3x dollars per unit. (a) Find the break-even points. (Enter your answers as a comma-separated list.) x = 28.1300 (b) Find the maximum revenue. (Round your answer to the nearest cent.) (c) Form the profit function, P(x), from the cost and revenue functions. P(x) = (d)Find maximum profit. (Round your answer to the nearest cent.) $ (d) What price will maximize the profit? (Round your answer to the nearest cent.) $

Explanation / Answer

b) here revenue R=quantity *selling price =x*(1772-2x/3)=1772x-2x2/3

differentiating above with respect to x:

(d/dx)R =1772-4x/3

putting above eqauls to 0;

x=1329

therefore maximum revenue =1772*1329-2*(1329)2/3 =1177494

c) P(X)=Revenue -cost =x*(1772-2x/3-444-x/3)-36400 =x*(1328-x)-36400

P(x)=1328x-x2-36400

differntiating above with respect to x and putting above to 0;

x=664

therefore maximum profit =1328*664-(664)2-36400=404496

and price for which maximum profit occurs =664

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

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