Aire-Co produces home dehumidifies at two different plants in Atlanta and Phoeni

Question

Aire-Co produces home dehumidifies at two different plants in Atlanta and Phoenix. the per-unit cost of production in Atlanta and Phoenix is $400 and $360, respectively. Each plant can produce a maximum of 300 units per month. Inventory holding costs are assessed at $30 per unit in beginning inventory each month. Current inventory is 20 units. Aire-Co estimates the demand for its product to be 300, 400, and 500 units, respectively, over the next three months. Aire-Co wants to be able to meet this demand at minimum cost.

Formulate this problem as an LP model in a spreadsheet and solve using Solver.

How many dehumidifiers should be built in Atlanta, next month? How many in Phoenix?

Explanation / Answer

Let x1, x2, and x3 be the quantity to produce at Atlanta for months 1,2, and 3; Let y1, y2, and y3 be the quantity to produce at Phoenix for months 1,2, and 3; cost of production is 400(x1+x2+x3)+360(y1+y2+y3) x1+y1 must be >=300, x2+y2 >=400, x3+y3>=500 inventory at beginning fo month 2 is (x1+y1-300) with cost (x1+y-300)*30 inventory at beginning of month 3 is (x1+y1+x2+y2-300-400) with cost 30*(x1+y1+x2+y2-700) inventory at beginning of month 4 is (x1+y1+x2+y2+x3+y3-1200) with cost 30 times this Objective is to minimize the total production cost plus total inventory cost Obvious additional constraints are all x's and y's must be >=0

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