Question

To prepare for the Ramadhan month, Lula supermarket must determine the how many breads that the supermarket must stock. There are three types of breads that the supermarket is considering, i.e. bread A, B and C. The cost of per unit of each bread is shown in the Table below.

Brea/ Cost (SAR/unit) A 1.5 B 0.9 C 0.5

The supermarket has allocated a budget of SAR 2,000 for the breads. The selling price of bread A, B and C is SAR 3, SAR 2.5 and SAR 1.75 per unit, respectively. From last year data, the predicted maximum demand of bread A, B and C is 400, 500 and 300 units, respectively. The supermarket has a capacity of 1,000 units of bread and the manager want to stock up completely.

[3 Marks] Formulate a linear programming model for this problem to determine the number of units of each bread to order so as to maximize profit

Answer 1

Let, us consider

X1= No of Bread type A to be stocked

X2= No of Bread type B to be stocked

X3= No of Bread type C to be stocked

Objective function= Max Z= 1.5 *X1+1.6*X2+1.25*C (Profit for stocking each type of bread)
S.T

1.5 *X1+0.9*X2+0.5*X3 <=2000 (Budget is limited to 2000 for all of the purchases )

X1 <=400

X2 <=500

X3 <=300

X1+X2+X3 = 1000 ( Max only 1000 units can be stocked)

Max Profit obtained by stocking 1000 pieces of bread of all three types is 1525

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