A clothing company produces two goods namely pants (P) and sweaters (S) whose combined cost function is C = 6P2 + 10S2 − PS + 30. In a day, the clothing company is limited by a production quota of 34 units of output only. In equation form: P + S = 34 1. State the cost minimization problem of the clothing company. 2. Set-up the Lagrange equation and determine the quantity of pants (P) and sweaters (S) that the firm should produce daily to minimize cost. 3. What is the effect on cost if the company decides to increase the production quota by 1 more unit?
A clothing company produces two goods namely pants (P) and sweaters (S) whose combined cost function is C = 6P2 + 10S2 − PS + 30. In a day, the clothing company is limited by a production quota of 34 units of output only. In equation form: P + S = 34 1. State the cost minimization problem of the clothing company. 2. Set-up the Lagrange equation and determine the quantity of pants (P) and sweaters (S) that the firm should produce daily to minimize cost. 3. What is the effect on cost if the company decides to increase the production quota by 1 more unit?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Constrained Optimization using Lagrange Multiplier: Cost Minimization
A clothing company produces two goods namely pants (P) and sweaters (S) whose combined cost function is C = 6P2 + 10S2 − PS + 30.
In a day, the clothing company is limited by a production quota of 34 units of output only. In
equation form: P + S = 34
1. State the cost minimization problem of the clothing company.
2. Set-up the Lagrange equation and determine the quantity of pants (P) and sweaters (S) that the firm should produce daily to minimize cost.
3. What is the effect on cost if the company decides to increase the production quota by 1 more unit?
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