# Math assignment help

Week 6 Page 1 of 2

- A company produces two products that are processed on two assembly lines. Assembly line 1 has 100 available hours, and assembly line 2 has 42 available hours. Product 1 requires 10 hours of processing time on line 1 and product 2 requires 14 hours of processing on line 1. , On line 2, product 1 requires 7 hours and product 2 requires 3 hours. The profit for product 1 is $6 per unit, and the profit for product 2 is $4 per unit.
- Formulate a linear programming model for this problem.
- Solve the model by using graphical analysis.

- The Pinewood Furniture Company produces chairs and tables from two resources – labor and wood. The company has 80 hours of labor and 36 board-ft. of wood available each day. Demand for chairs is limited to 6 per day. Each chair requires 8 hours of labor and 2 board-ft. of wood, whereas a table requires 10 hours of labor and 6 board-ft. of wood. The profit derived from each chair is $400 and from each table, $100. The company wants to determine the number of chairs and tables to produce each day in order to maximize profit. Formulate a linear programming model for this problem.
- Formulate a linear programming model for this problem.
- Solve the model by using graphical analysis.

- In Problem 2, how much labor and wood will be unused if the optimal numbers of chairs and tables are produced?
- The Elixer Drug Company produces a drug from two ingredients. Each ingredient contains the same three antibiotics, in different proportions. One gram of ingredient 1 contributes 3 units and one gram of ingredient 2 contributes 1 unit of antibiotic 1; the drug requires 6 units. At least 4 units of antibiotic 2 are required and the ingredients contribute 1 unit each per gram. At least 12 units of antibiotic 3 are required; a gram of ingredient 1 contributes 2 units, and a gram of ingredient 2 contributes 6 units. The cost for a gram of ingredient 1 is $80, and the cost for a gram of ingredient 2 is $50. The company wants to formulate a linear programming model to determine the number of grams of each ingredient that must go into the drug in order to meet the antibiotic requirements at the minimum cost.
- Formulate a linear programming model for this problem.
- Solve the model by using graphical analysis.

5. A clothier makes coats and slacks. The two resources required are wool cloth and labor. The

MAT540 Homework Week 6 Page 2 of 2

clothier has 150 square yards of wool and 200 hours of labor available. Each coat requires 3 square yards of wool and 10 hours of labor, whereas each pair of slacks requires 5 square yards of wool and 4 hours of labor. The profit for a coat is $50, and the profit for slacks is $40. The clothier wants to determine the number of coats and pairs of slacks to make so that profit will be maximized.

- Formulate a linear programming model for this problem.
- Solve the model by using graphical analysis.

6. Solve the following linear programming model graphically: Maximize Z = 5×1 + 8×2

Subject to 4×1 +5×2 ≤50 2×1 +4×2 ≤40 x1 ≤ 8

x2 ≤ 8

x1, x2 ≥ 0

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