"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.

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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step-by-step explanation:

answer: there are x+184 pages in olivia's book.

step-by-step explanation:

let the total number of pages in the book which olive has already read be x.

then if olive has 184 pages left to read, then the total number of pages are in olive's book= pages she has read+pages she has left to read

therefore, the total number of pages in olivia's book=

hence, there are x+184 pages in olivia's book.