1. Qatar Chemical Company (QCC) manufactures its product in two plants, A and B,

Question

1. Qatar Chemical Company (QCC) manufactures its product in two plants, A and B, and sells its product in four markets Qatar, Saudi Arabia, Bahrain and United Arab Emirates The capacity in Plant A is 300 units and in Plant B 350 units. The demands and shipping costs for the four markets are tabled below United Arab Qatar 155 10 Saudi Arabia 230 20 15 Bahrain 225 15 10 Emirates 160 25 20 Demand Shipping costs from Plant A Shipping costs from Plant B The usual per-unit labor cost is $95 in either plant. The other costs per-unit are $50 in Plant A and $70 in Plant B. Overtime labor can be hired only at Plant A at a per unit cost of $140. If the capacity is not adequate to meet the demand, additional items can be manufactured at Plant A using overtime labor (4 points) Formulate a linear programming problem that will be used to determine how QCC should schedule its production to meet all demand while minimizing its total costs (Do not solve the linear program). a)

Explanation / Answer

LP model is as under

Decision variables:

Let A1, A2, A3, A4 be the number of units produced in regular time in plant A and shipped to the four markets (Qatar, Saudi, Bahrain, UAE resp)

Let X1, X2, X3, X4 be the number of units produced in overtime in plant A and shipped to the four markets (Qatar, Saudi, Bahrain, UAE resp)

Let B1, B2, B3, B4 be the number of units produced in plant B and shipped to the four markets (Qatar, Saudi, Bahrain, UAE resp)

Objective:

Min (95+50)*(A1+A2+A3+A4)+(95+70)*(B1+B2+B3+B4)+(140+50)*(X1+X2+X3+X4)+10*(A1+X1)+20*(A2+X2)+15*(A3+X3)+25*(A4+X4)+5B1+15B2+10B3+20B4

Constraints:

s.t.

A1+X1+B1 = 155

A2+X2+B2 = 230

A3+X3+B3 = 225

A4+X4+B4 = 160

A1+A2+A3+A4 <= 300

B1+B2+B3+B4 <= 350

All variables >= 0

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