MA 160 Section 2.6 Worksheet
Further Optimization, Inventory
Name __________________________________
Date _____________________________
1. The Great American Tire Co. expects to sell 600,000 tires of a particular size and grade during
the next year. Sales tend to be roughly the same from month to month. Setting up each production
run costs the company $15,000. Carrying costs, based on the average number of tires in storage,
amount to $5 per year for one tire. Find the economic lot size (i.e. the production run size that
minimizes the overall cost of producing the tires).
a. What quantity is to be maximized or minimized?
b. Assign letters to the variables.
c. What is the objective function?
d. What is the constraint equation?
e. Express the objective function in terms of one variable and determine its domain.
f. Use the first or second derivative test to solve the problem.
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2. A supermarket is to be designed as a rectangular building with a floor area of 12,000 square feet.
The front of the building will be mostly glass and will cost $70 per running foot for materials. The
other three walls will be constructed of brick and cement block, at a cost of $50 per running foot.
Ignore all other costs (labor, cost of foundation and roof, etc.) and find the dimensions of the base of
the building that will minimize the cost of the materials for the four walls of the building.
a. What quantity is to be maximized or minimized?
b. Make a sketch and assign letters to the variables.
c. What is the objective function?
d. What is the constraint equation?
e. Express the objective function in terms of one variable and determine its domain.
f. Use the first or second derivative test to solve the problem.
Answers: 1. Each run should produce 60,000 tires.
2. The glass front is 100 feet and the other dimension is 120 feet.
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