The cost, in dollars, fo producing x yards of a certain fabric is C(x) = 1500 +

Question

The cost, in dollars, fo producing x yards of a certain fabric is C(x) = 1500 + 15x - 0.1x^2 + 0.0005x^3. (a) Find the marginal cost function. C'(x) = (b) Find C'(500) and explain its meaning, what does it predict? C'(500) = and this is the rate at which costs are increasing with respect to the production level when x = C'(500) predicts the cost of producing the yard. (c) Compare C'(500) with the cost of manufacturing the 501st yard of fabric. The cost of manufacturing the 501st yard of fabric is C(501) - C(500) = -46, 500 = which is approximately cC'(500).

Explanation / Answer

Sol (a) To get the marginal cost function we differentiate C'(x) with respect to x and we have
  C'(x) = 15- 0.2x + 0.0015x²

Sol (b) C'(500) = 15 - 0.2*500 + 0.0015* (500)2 = 15 -100 + 375 = 290

C'(500) = 290 and this is the rate at which costs are increasing with respect to the production level when x = -63.98 ( which we are getting after solving equation 0.0005x2 - 0.1 x2 +15x +1500 =0)
C'(500) predict the cost of producing 500 yards

Sol (c) C(501) - C(500) = 46790.65 46500 = 290.65 which is approx C'(500) = 290 (calculated above)
C(501) = 1500 + 15 *501 - 0.1 * 5012 + 0.0005* (501)3
= 1500 + 7515 - 25100.1 + 62875.75 = 46790.65

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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