Formulation of Linear program (LP) to maximize the revenue from candy sales:

Let “x_ij” be the ounces of ingredient “i” used to make candy “j”.

Let ingredient 1 is sugar, 2 is nuts, and 3 is chocolate. The candy 1 is slugger candy and 2 is easy out candy.

The objective of function is to maximize the revenue from the candy sales.

Each ounce of out candy can be sold for 25 cents and each ounce of slugger candy can be sold for 20 cents.

Therefore, the objection function is,

Maximize, z=25(x12+x22+x32)+20(x11+x21+x31)

Constraint 1:

At present, 100 oz of sugar is in the stock.

Ounces of sugar in slugger candy + ounces of sugar in easy out candy ≤ 100x11+x12≤100

Constraint 2:

At present, 20 oz of nuts is in the stock.

Ounces of nuts in slugger candy + ounces of nuts in easy out candy ≤ 20x21+x22≤20

Constraint 3:

At present, 30 oz of nuts is in the stock.

Ounces of chocolate in slugger candy + ounces of chocolate in easy out candy ≤ 30x31+x32≤30

Constraint 4:

At least, 20% of nuts must be there in easy out candy.

20% of nuts in easy out candy ≥0.2

x22≥0.2(x12+x22+x32)

Constraint 5:

At least, 10% of nuts must be there in slugger candy.

10% of nuts in slugger candy ≥0.1

x21≥0.1(x11+x21+x31)

Constraint 6:

At least, 10% of chocolate must be there in slugger candy

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Chapter 3 Solutions

Introduction to mathematical programming

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