Question
Your weekly cost (in dollars) to manufacture $x$ bicycles and $y$ tricycles is$$C(x, y)=24,000+60 x+20 y$$Calculate and interpret $\frac{\partial C}{\partial x}$ and $\frac{\partial C}{\partial y}$.
Step 1
This means we are finding the rate of change of the cost with respect to the number of bicycles manufactured, while keeping the number of tricycles constant. Show more…
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Your weekly cost (in dollars) to manufacture $x$ cars and $y$ trucks is $$ C(x, y)=240,000+6,000 x+4,000 y $$ Calculate and interpret $\frac{\partial C}{\partial x}$ and $\frac{\partial C}{\partial v}$. HINT [See Example 1.]
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Your weekly cost (in dollars) to manufacture $x$ bicycles and $y$ tricycles is $$ C(x, y)=24,000+60 x+20 y+0.3 x y $$ (Compare with Exercise 78.) Compute the marginal cost of manufacturing tricycles at a production level of 10 bicycles and 20 tricycles. HINT [See Example 2.]
Your weekly cost (in dollars) to manufacture x bicycles and y tricycles is C(x, y) = 36,000 + 90x + 40y. Calculate and interpret ∂C/∂x and ∂C/∂y. The marginal cost to manufacture bicycles is the partial derivative of C with respect to x, which is dollars per bicycle. The marginal cost to manufacture tricycles is the partial derivative of C with respect to y, which is dollars per tricycle. The marginal costs do not depend on the production level, since the cost function is linear.
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