Statistics: Linear Programming

LINEAR PROGRAMMING
1. Find the complete (including values for slack variables) optimal solution to this linear programming problem using. graphical method

Min 5X + 6Y
s.t. 3X + Y > 15
X + 2Y > 12
3X + 2Y > 24
X , Y > 0

2. Find the complete (including values for slack variables) optimal solution to this linear programming problem using Excel Solver or QM for Windows.

Max 5X + 3Y
s.t. 2X + 3Y < 30
2X + 5Y < 40
6X - 5Y < 0
X , Y > 0

3. Formulate and solve the following problem. Use method of your choice.

The Marketing Club at your college has decided to raise funds by selling three types of T-shirts: one with single-color "ordinary" design, one with a two-color "fancy" design, and one with a three-color "very fancy" design. The club feels that it can sell up to 300 T-shirts. "Ordinary" T-shirts will cost the club $6 each, "fancy" T-shirts $8 each, and "very fancy" T-shirts $10 each, and the club has a total purchasing budget of $3,000. It will sell "ordinary" T-shirts at profit of $4 each, "fancy" T-shirts at profit of $5 each, and "very fancy" T-shirts at a profit of $4 each. How many of each kind of T-shirt should the club order to maximize profit?

4. Formulate and solve the following problem. Use method of your choice.

The production manager for Beer etc. produces 2 kinds of beer: light (L) and dark (D). Two resources used to produce beer are malt and wheat. He can get at most 4800 oz of malt per week and 3200 oz of wheat per week. Each bottle of light beer requires 12 oz of malt and 4 oz of wheat, while a bottle of dark beer uses 8 oz of malt and 8 oz of wheat. Profits for light beer are $2 per bottle, and profits for dark beer are $1 per bottle. What is the linear programming model for this problem?