You have decided to enter the candy business. You are considering producing two

Question

You have decided to enter the candy business. You are considering producing two types of candies: Slugger candy and Easy Out candy, both of which consist solely of sugar, nuts, and chocolate. At present you have in stock 10,000 ounces of sugar, 2,000 ounces of nuts, and 3,000 ounces of chocolate. The mixture used to make Easy Out candy must contain at least 20% nuts. The mixture used to make Slugger candy must contain at least 10% nuts and 10% chocolate. Each ounce of Easy Out candy can be sold for $0.50, and each ounce of Slugger candy for $0.40. Develop a linear program to determine how you can maximize your revenue from candy sales.

Explanation / Answer

Let the ounces of slugger candy be "x" and easy candy be "y"

Then the linear program will be:

Revenues = 0.4x+0.5y. We have to maximize this equation, subject to the constraints -

Slugger candy's requirement is 10% nut and 10% chocolate (atleast) and remaining (100-20) 80% sugar.

Easy candy's requirement is 20% nuts (atleast) remaining 80% should be of sugar and chocolate.

So, requirement for nuts = 0.10x+0.20y

0.10x+0.20y<, equal to 2,000

We keep the requirement for sugar and chocolate as blank as they can be used in any ratio in easy out candy.

The following is the solution as per solver in excel:

So revenue is 6,500 by selling 5,000 ounces of easy candy and 10,000 ounces of slugger.

The model fed in excel (before solver being used is):

The objective is to maximize Revenue, by changing the cells of quantity of easy and slugger sold and quantity of sugar and chocolate used in easy candy.

Constraints put were:

Total sugar used should be <equal to 10,000

total nuts used should be <equal to 2,000

total chocolate used should be <equal to 3,000

Easy Slugger Total Easy Slugger sugar 0.4 0.8 10,000.0 10,000.0 0.5 0.4 nuts 0.2 0.1 2,000.0 2,000.0 quantity 5,000.0 10,000.0 chocolates 0.4 0.1 3,000.0 3,000.0 revenue 6,500.0 1.0

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