Question

Operartion reasearch course

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.

Bread	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.

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

Answer:

Decision Variables:

Let the decision variables:

a = no. of units of bread A to be ordered

b = no. of units of bread B to be ordered

c = no. of units of bread C to be ordered

Objective Function:

Here, an objective is to maximize the total profit, hence an objective function would be:

Max Z = Total Profit = Total Sales - Total Cost

= (3 a + 2.5 b + 1.75 c) - ( 1.5 a + 0.9 b + 0.5 c)

Hence, Max Z = 1.5 a + 1.6 b + 1.25 c

Subject to Constraints:

Budget Constraint:

1.5 a + 0.9 b + 0.5 c ≤ 2000

Demand Constraint:

a ≤ 400

b ≤ 500

c ≤ 300

Full Capacity Utilization

a + b+ c = 1000

Non-Negativity Condition:

a, b, c ≥ 0

Hence, we get a complete LP model as mentioned below:

Max Z = 1.5 a + 1.6 b + 1.25 c

Subject to,

1.5 a + 0.9 b + 0.5 c ≤ 2000

a ≤ 400

b ≤ 500

c ≤ 300

a + b+ c = 1000

a, b, c ≥ 0

[ Note: As no specific information is mentioned in the question, here, we will just formulate an LP model (no need to solve) ]