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The Jersey Chemical Company manufactures two industrial chemical products, called Zanide and Kreolite. Two machines are...

The Jersey Chemical Company manufactures two industrial chemical products, called Zanide and Kreolite. Two machines are used in the process, and each machine has 24 hours of capacity per day. The following data are available:

Zanide

Kreolite

Selling price per drum

$36

$42

Variable cost per drum

$28

$28

Hours required per drum on machine I

2 hours

2 hours

Hours required per drum on machine II

1 hour

3 hours

The company can produce and sell partially full drums of each chemical. For example, a half drum of Zanide sells for $18.

Required:

  1. Formulate the product mix problem as a linear program.
  2. Solve the problem graphically.
  3. What is the value of the objective function at the optimal solution?

Solutions

Expert Solution

  1. Formulate the product mix problem as a linear program.

-Formulate the Product mix, also known as product assortment or product portfolio, refers to the complete set of products and/or services offered by a firm. A product mix consists of product lines, which are associated items that consumers tend to use together or think of as similar products or services.

1- calculation the unit contributions of Zanide and Kreilite -

The unit contribution - selling price - variable cost

for Zanide ($36-28)=$8

for Kreolite ($42-28)=$14

Thus the decision problem is to maximize the combined contribution of Zanide and krelite.

This is represented by the objectives functions.

  1. What is the value of the objective function at the optimal solution?

optimal solution is a feasible solution where the objective function reaches its maximum (or minimum) value – for example, the most profit or the least cost. A globally optimal solution is one where there are no other feasible solutions with better objective function values.

A globally optimal solution is one where there are no other feasible solutions with better objective function values. A locally optimal solution is one where there are no other feasible solutions “in the vicinity” with better objective function values – you can picture this as a point at the top of a “peak” or at the bottom of a “valley” which may be formed by the objective function and/or the constraints.

ekkarill92 answered 1 year ago
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