(Q7: see reference of Q4 for marginal value method to solving profit max problem)7. a. Use calculus to find the profit maximizing level of (a) output, (b) price, and (c) profit for atwo-product firm facing the following demand and cost functions (hint: marginal method):P₁ = 475-601P2 = 450-802TC(Q1Q2)=40+5Q1Q2 +30 +700where quantities are expressed on a weekly basis.b. Check your answer with excel solver.(Q8: refer to Q3 and Q5 for constrained optimization problem, also see Q4 of PS 5-B)8. Suppose the firm in problem 7 has a maximum joint capacity of 40 units per week(Q1+Q2<=40).a. Use Solver to find the profit maximizing level of output, price, and profit given thisproduction constraint.b. Use the Lagrange multiplier (sensitivity report) to estimate the effect of expandingcapacity by one more unit per week.

Demand functions:Cost function**Since you have posted multiple questions, we will answer the first…

7. a. Use calculus to find the profit maximizing level of (a) output, (b) price, and (c) profit for a two-product firm facing the following demand and cost functions (hint: marginal method): P₁ = 475-6Q1 P2 = 450-802 TC(Q1Q2)=4Q+5Q1Q2 +30 +700 where quantities are expressed on a weekly basis. b. Check your answer with excel solver.

7. a. Use calculus to find the profit maximizing level of (a) output, (b) price, and (c) profit for a two-product firm facing the following demand and cost functions (hint: marginal method): P₁ = 475-6Q1 P2 = 450-802 TC(Q1Q2)=4Q+5Q1Q2 +30 +700 where quantities are expressed on a weekly basis. b. Check your answer with excel solver.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

(Q7: see reference of Q4 for marginal value method to solving profit max problem)
7. a. Use calculus to find the profit maximizing level of (a) output, (b) price, and (c) profit for a
two-product firm facing the following demand and cost functions (hint: marginal method):
P₁ = 475-601
P2 = 450-802
TC(Q1Q2)=40+5Q1Q2 +30 +700
where quantities are expressed on a weekly basis.
b. Check your answer with excel solver.
(Q8: refer to Q3 and Q5 for constrained optimization problem, also see Q4 of PS 5-B)
8. Suppose the firm in problem 7 has a maximum joint capacity of 40 units per week
(Q1+Q2<=40).
a. Use Solver to find the profit maximizing level of output, price, and profit given this
production constraint.
b. Use the Lagrange multiplier (sensitivity report) to estimate the effect of expanding
capacity by one more unit per week.

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