Formulate a linear programming model for the below set of problems. For those problems, solve the linear programming model by using the computer. You can use either QM for Windows or Solver (in Excel) to solve these problems.
If using QM for Windows, you can capture the results and a graph in one of two ways:
- By doing a "Print Screen," you capture the screen image. You can now copy directly to Word (or to Paint, and then to Word).
- Or you can save data from QM for Windows as an HTML file. You can only save data one window at a time. Highlight the QM for Windows output window you want to save and select Save As HTML. You can then edit the HTML file in Word to your liking, or you can copy it directly to Word.
If you use QM for Windows, please include the results screen and the Graph in the Word document you create. Follow the format of the examples that were posted in the Doc Sharing tab. Include the model formulation or a window showing the constraints. Save the resulting file as a Word file.
If using Solver, please submit the Excel file (include the model formulation on the worksheet). If using an Excel document, put one problem per worksheet, label all worksheets and put all problems in one file.
Problem 1
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. Each product requires 10 hours of processing time on line 1, while on line 2 products 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.
Problem 2
A company makes fertilizer using two chemicals that provide nitrogen, phosphate and potassium. A pound of ingredient 1 contributes 10 ounces of nitrogen and 6 ounces of phosphate, while a pound of ingredient 2 contributes 2 ounces of nitrogen, 6 ounces of phosphate, and I ounce of potassium. Ingredient 1 costs $3 per pound and ingredient 2 costs $5 per pound. The company wants to know how many pounds of each chemical ingredient to put into a bag of fertilizer to meet the minimum requirements of 20 ounces of nitrogen, 36 ounces of phosphate, and 2 ounces of potassium while minimizing cost.
Problem 3
A drug company produces drug from two ingredients. Each ingredient contains the same three antibiotics, in different proportions. One gram of ingredient 1 contributes 3 units and 1 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 each contribute 1 unit 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.
Problem 4
A clothier makes coats and slacks. The two resources required are wool cloth and labor. The clothier has 150 square yards of wool and 200 hours of labor available. Each cost 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 profit for slacks is $40. The clothier wants to determine the number of coats and pair of slacks to make so that profit will be maximized.