Question
Repeat the preceding exercise using the weekly cost to manufacture $x$ bicycles and $y$ tricycles given by$$C(x, y)=24,000+60 x+20 y+0.3 x y$$(Compare with Exercise $78 .$ )
Step 1
The marginal cost is the derivative of the cost function with respect to the quantity of the product. Show more…
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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.]
Functions of Several Variables
Partial Derivatives
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 $\frac{\partial C}{\partial y}$.
Your weekly cost (in dollars) to manufacture $x$ bicycles and $y$ tricycles is $$ C(x, y)=24,000+60 x+20 y $$ a. What is the marginal cost of a bicycle? Of a tricycle? HINT [See Example 1.] b. Describe the graph of the cost function $C$. HINT [See Example 7.] c. Describe the slice by $y=100 .$ What cost function does this slice describe? d. Describe the level curve $z=72,000$. What does this curve tell you about costs?
Functions of Several Variables from the Numerical, Algebraic, and Graphical Viewpoints
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