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The Hardgrave Machine Company produces computer components at its plants in Kingston, ON; Prince George, BC; and Sudbury, ON. These plants supply the demand for orders at Hardgrave's two warehouses in Hamilton and Regina.
The tables below present the information of: (i) the production cost and capacity for each of the three plants, and the demand at each of the two warehouses
Production Plant
Monthly Supply (units)
Production Cost per Unit ($)
Kingston
15,000
$50
Prince George
20,000
$55
Sudbury
25,000
$45
Warehouse
Monthly Demand (Units)
Hamilton
35,000
Regina
30,000
Transportation costs per unit from each plant to each warehouse are summarized in the following table:
To:
From:
$10
$25
$15
$20
$30
Recent regulations require that no more than 8,000 units are to be shipped from the plant in Kingston to the Warehouse located in Hamilton. Also, at least 30% of the total computer components shipped to the warehouse in Regina are from the plant in Prince George.
Formulate algebraically the above problem to help Hardgrave satisfy the demand at the warehouses at the lowest production and transportation costs. Define the decision variables, objective function, and constraints. DO NOT SOLVE.
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