Question

Problem formulation:

The company wants to increase the availabel sortiment from 2 types of glasses to 3 types. A production

line already produces 2 different types of glasses: 6oz juice glasses and 10oz cocktail glasses and 8oz

champagne glass. Adding a new type is possible but you as a manager should check that it will be cost

effective. The production line can produce 100 cases of 6oz glasses in 6 hours and 100 cases of 10oz glasses

in 5 hours. The production time for the new type, a champagne glass, is 8 hours per 100 cases. A manager

needs to optimize the production while she prefers to operate the line on a schedule of 60 hours per week.

The product is stored in factory’s storage room with the capacity of 15000 cubic feet. A case of 6oz glasses

requires 10 cubic feet and a case of 10oz glasses requires 20 cubic feet. A case of the 8oz champagne glass

requires 10 cuft. A retail customer will buy 6oz glasses for $5.00 per case but can accept only 800 cases per

week and 10oz glasses for $4.50 per case, and 8oz glasses for $6.00 per case and there is no limit on the size

of the order for these two types.

Tasks:

1.Find how how many cases of each type of glass should be produced each week in order to

maximize the profit ?

Note: In the report display the optimal solution and the objective function value clearly in a form of

a table.

2. Is including a new type of glass (the champagne glass) economically attractive ?

3. Determine shadow prices summarize them in a table and associate correct units with them.

4. If you divert resources to produce extra one hundred cases of 8oz champagne glasses how

much would the profit change ? (this quantity is called reduced cost).

Answer 1