Question 1
Johnson City Cooperage manufactures 30-gallon and 55-gallon fibre drums. Each 30-gallon drum
takes 30 minutes to make, each 55-gallon drum takes 40 minutes to make, and the company has at
most 10,000 minutes available each week. The workplace limitations indicate that the number of
55-gallon drums produced plus half the number of 30-gallon drums produced should be at least
160. Also, product demand indicates that the number of 30-gallon drums should be at least twice
the number of 55-gallon drums. If Johnson City Cooperage’s manufacturing costs are $4 for each30-gallon drum and $6 for each 55-gallon drum, how many of each drum should be made each
week to satisfy the constraints at minimum cost?
(a) Formulate the linear programming (LP) problem that minimizes cost.
(b) Graph the feasible region.
(c) Using the method of corner points, find how many sets of each type should be produced so
that the company has a minimize cost.
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