“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 pro

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.

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Harper 1 week 2021-09-13T22:32:59+00:00 1 Answer 0

Answers ( )

  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

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