Problem formulation: The company wants to increase the available 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. Adding a new type, 8oz champagne glass, 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 8oz 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. The decision about production of individual glasses requires to maximize the profit. 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 ? State clearly the optimization problem to be solved before proceeding to the solution. 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)