Problem #1 (20 points) A production manager wants to determine how many units of each product to produce weekly to maximize weekly profits. Production requirements for the products are shown in the following table.

Material 1 costs $7 a pound, material 2 costs $5 a pound, and labor costs $15 per hour. Product A sells for $101 a unit, product B sells for $67 a unit, and product C sells for $97.50 a unit. Each week there are 300 pounds of material 1; 400 pounds of material 2; and 200 hours of labor. Also, there is a weekly demand of at least 10 units of product C each week.

Formulate the given problem scenario as a linear program, and setup/solve the problem using Microsoft Excel with Analytic Solver (or Open Solver). For the mathematical formulation, provide a complete mathematical description of the decision variables (with units), objective function and constraints. You should use explicit (or implicit) form. Also, the spreadsheet model setup should provide clearly labeled values used for the decision variables, constraints, and objective function. Please show the formulas in each cell.

Product A B Material 1 (lbs.) 3 1 5 Material 2 (lbs.) 2 4 Labor (hours) 4 2 3.5 none