The profit made by selling q1 units of product 1 and q2 units of product 2 is given by P(q1,q2)=200q1 −3q12 +100q2 −q2 −2q1q2 (a) Calculate ∂P (20, 15) and ∂P (20, 15). ∂q1 ∂q2 (b) Describe the graphical meaning of these two numbers. (c) Describe the economic meaning of these two numbers. (d) Find a linear function g(q1, q2) that can be used as an approximation for the function P (q1, q2) for values (q1,q2) close to (20,15). Explain how the function g(q1,q2) relates to the function P(q1,q2) graphically. What is the mathematical name of the approximating function g? (e) Use the linear function you found in part d to estimate the profit made by selling 18 units of product 1 and 16 units of product 2. Compare to the exact value of the profit.
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The profit made by selling q1 units of product 1 and q2 units of product 2 is given by P(q1,q2)=200q1 −3q12 +100q2 −q2 −2q1q2
(a) Calculate ∂P (20, 15) and ∂P (20, 15). ∂q1 ∂q2
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(b) Describe the graphical meaning of these two numbers.
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(c) Describe the economic meaning of these two numbers.
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(d) Find a linear function g(q1, q2) that can be used as an approximation for the function P (q1, q2) for values (q1,q2) close to (20,15). Explain how the function g(q1,q2) relates to the function P(q1,q2) graphically. What is the mathematical name of the approximating function g?
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(e) Use the linear function you found in part d to estimate the profit made by selling 18 units of product 1 and 16 units of product 2. Compare to the exact value of the profit.
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