Linear Programming: Maximize Profit for Biscuit Manufacturer

[sauravbhaumik]

Please help:

A manufacturer of biscuits is considering three types of gift packs
containing three types of biscuits, Orange Cream (OC), Chocolate
Cream(CC) and Wafers (W). Market research study conducted recently
shows that three types of assortments A, B and C are in good demand.
Assortment A contains not less than 40% of OC, not more than 20% of CC
and any quantity of W. Assortment B contains not less than 20% of OC,
not more than 40% of CC and any quantity of W. Assortment C has no
restriction. The selling price per kg of assortments A, B and C are
respectively Rs200, Rs 250 and Rs 120. The manufacturing capacity per
day of OC, CC and W respectively 200Kg, 200 kg and 150 kg. The
manufacturing costs per kg of OC, CC and W are respectively Rs 80, Rs
90 and Rs 70. Formulate a linear programming model to find the production
schedule which maximizes the profit.

 

[D H]

This tastes like homework. You should have posted this in the homework section. Have you read the rules on homework? In particular, you need to show some work before people will help you. We won't simply do you your work for you.

 

[tacman]

To maximize the profit for the biscuit manufacturer, the linear programming model should include the following variables:

X1 = kg of assortment A produced per day
X2 = kg of assortment B produced per day
X3 = kg of assortment C produced per day

The objective function would be to maximize the total profit, which can be expressed as:

Maximize Z = 200X1 + 250X2 + 120X3

Next, we need to consider the constraints given in the problem:

1. The total production capacity for Orange Cream is 200 kg per day. This means that the total production of Orange Cream should not exceed 200 kg per day. This can be expressed as:

X1 ≤ 200

2. The total production capacity for Chocolate Cream is 200 kg per day. This means that the total production of Chocolate Cream should not exceed 200 kg per day. This can be expressed as:

X2 ≤ 200

3. The total production capacity for Wafers is 150 kg per day. This means that the total production of Wafers should not exceed 150 kg per day. This can be expressed as:

X1 + X2 + X3 ≤ 150

4. The percentage of Orange Cream in Assortment A should be at least 40%. This can be expressed as:

X1 ≥ 0.4(X1 + X2)

5. The percentage of Orange Cream in Assortment B should be at least 20%. This can be expressed as:

X2 ≥ 0.2(X1 + X2)

6. The percentage of Chocolate Cream in Assortment A should be no more than 20%. This can be expressed as:

X2 ≤ 0.2(X1 + X2)

7. The percentage of Chocolate Cream in Assortment B should be no more than 40%. This can be expressed as:

X1 ≤ 0.4(X1 + X2)

8. As per the market research, there are no restrictions on the composition of Assortment C. This can be expressed as:

X1 + X2 + X3 ≥ 0

Finally, all the variables should be non-negative, which can be expressed as:

X1, X2, X3 ≥ 0

Therefore, the linear programming model to maximize the profit for the biscuit manufacturer can be formulated as:

Maximize Z = 200X1 +