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. (10 points) 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. (3 points) Is including a new type of glass (the champagne glass) economically attractive? 3. (5 points) Determine shadow prices summarize them in a table and associate correct units with them. 4. (2 points) 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).