Question

(Marginal cost) The cost of manufacturing $x$ refrigerators is $\mathrm{SC}(x)$, where $$ C(x)=8,000+400 x-0.5 x^{2} $$ (a) Find the marginal cost if 100 refrigerators are manufactured. (b) Show that the marginal cost is approximately the difference in cost of manufacturing 101 refrigerators instead of 100.

          (Marginal cost) The cost of manufacturing $x$ refrigerators is $\mathrm{SC}(x)$, where
$$ C(x)=8,000+400 x-0.5 x^{2} $$
(a) Find the marginal cost if 100 refrigerators are manufactured.
(b) Show that the marginal cost is approximately the difference in cost of manufacturing 101 refrigerators instead of 100.

Added by Alicia S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

09/19/2023

Step 1

e., $\mathrm{MC}(x) = \frac{d}{dx} \mathrm{SC}(x)$. Using the given cost function, we have: $$\mathrm{SC}(x) = 8,000 + 400x - 0.5x^2$$ $$\mathrm{MC}(x) = \frac{d}{dx} \mathrm{SC}(x) = 400 - x$$ Substituting $x=100$, we get: $$\mathrm{MC}(100) = 400 - 100 = 300$$ Show more…

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(Marginal cost) The cost of manufacturing $x$ refrigerators is $\mathrm{SC}(x)$, where $$ C(x)=8,000+400 x-0.5 x^{2} $$ (a) Find the marginal cost if 100 refrigerators are manufactured. (b) Show that the marginal cost is approximately the difference in cost of manufacturing 101 refrigerators instead of 100.