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Statistics - Linear Programming

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Biggio's Department Store has six employees available to assign to four departments in the store: home furnishings, china, appliances, and jewelry. Most of the six employees have worked in each of the four departments on several occasions in the past and have demonstrated that they perfrom better in some departments than in others. The average daliy sales for each of the six employees in each of the four departments are shown in the following table:

Department Sales
Employee Home Furn China Appliances Jewelry
1 \$340 \$160 \$610 \$290
2 560 370 520 450
3 270 -- 350 420
4 360 220 630 150
5 450 190 570 310
6 280 320 490 360

Employee 3 has not worked in the china department before, so the manager does not want to assign this employee to china.

Using excel solver determine which employee to assign to each department and indicate total expected sales.

https://brainmass.com/statistics/general-linear-model/statistics-linear-programming-227136

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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?

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