Question

"The owner of Chips etc. produces two kinds of chips: lime (L) and vinegar (V). He has a limited amount of the three ingredients used to produce these chips available for his next production run: 4800 ounces of salt, 9600 ounces of flour, and 2000 ounces of herbs. A bag of lime chips requires 2 ounces of salt, 6 ounces of flour, and 1 ounce of herbs to produce; while a bag of vinegar chips requires 3 ounces of salt, 8 ounces of flour, and 2 ounces of herbs. Profits for a bag of lime chips are $0.40, and for a bag of vinegar chips $0.50"
Required:
What is the formulation for this problem? Suppose that L and V are the decision variables respectively of Lime and Vinegar.

Answer 1

Objective function (maximize)

Profit=0.40L+0.50V

Subject to the Constraints

- Availability of salt: 2L+3V ≤4800

- Availability of flour: 6L+8V≤9600

- Availability of herbs: 1L+2V≤2000

Explanation:

In this linear programming problem, our objective is to maximise (make profit) but complying with some constraints.

The profit for a bag of lime chips(L) is $0.40, and for a bag of vinegar chips(V) is $0.50.

Therefore:

Profit=0.40L+0.50V

Next, we determine the Constraints defined by the availability of materials.

Total available ounce of salt = 4800

A bag of Lime Chip(L) requires 2 ounces of salt and a Bag of vinegar chips(V) requires 3 ounces of salt.

Therefore:

2L+3V≤4800

Total available ounce of flour = 9600

A bag of Lime Chip(L) requires 6 ounces of flour and a Bag of vinegar chips(V) requires 8 ounces of flour.

Therefore:

6L+8V≤9600

Total available ounce of Herbs = 2000

A bag of Lime Chip(L) requires 1 ounce of herv and a Bag of vinegar chips(V) requires 2 ounces of flour.

Therefore:

1L+2V≤2000

Thus, the formulation of the linear programming problem is as follows.

Objective function (maximize)

Profit=0.40L+0.50V

Subject to the Constraints

- Availability of salt: 2L+3V ≤4800

- Availability of herbs: 1L+2V≤2000

- Availability of flour: 6L+8V≤9600