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1.) A warehouse orders and stores boxes. The cost of storing boxes is proportional to q, the quantity ordered. The cost of ordering boxes is proportional to 1/q, because the warehouse gets a price cut for larger orders. The total cost of operating the warehouse is the sum of ordering costs and storage costs. What value of q gives the minimum cost?

1.) A warehouse orders and stores boxes. The cost of storing boxes is proportional to q, the quantity ordered. The cost of ordering boxes is proportional to 1/q, because the warehouse gets a price cut for larger orders. The total cost of operating the warehouse is the sum of ordering costs and storage costs. What value of q gives the minimum cost?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Math 251 Classwork Ch. 6.5 1.) A warehouse orders and stores boxes. The cost of storing boxes is proportional to q, the quantity ordered. The cost of ordering boxes is proportional to 1/q, because the warehouse gets a price cut for larger orders. The total cost of operating the warehouse is the sum of ordering costs and storage costs. What value of q gives the minimum cost? 2.) Find the maximum area of a rectangle inscribed between the x-axis and f(x) = -x¹ +3. 3.) A rain gutter is made from a sheet of metal that is 30 cm wide. Each outter third of the sheet is bent up at the same angle to make the rain gutter. What angle should the sides of the metal sheet be bent at so that the gutter will carry the most water possible? 0 10 cm 10 cm 10 cm
Transcribed Image Text:Math 251 Classwork Ch. 6.5 1.) A warehouse orders and stores boxes. The cost of storing boxes is proportional to q, the quantity ordered. The cost of ordering boxes is proportional to 1/q, because the warehouse gets a price cut for larger orders. The total cost of operating the warehouse is the sum of ordering costs and storage costs. What value of q gives the minimum cost? 2.) Find the maximum area of a rectangle inscribed between the x-axis and f(x) = -x¹ +3. 3.) A rain gutter is made from a sheet of metal that is 30 cm wide. Each outter third of the sheet is bent up at the same angle to make the rain gutter. What angle should the sides of the metal sheet be bent at so that the gutter will carry the most water possible? 0 10 cm 10 cm 10 cm
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