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. Product Material 1 (lbs.) Material 2 (lbs.) Labor (hours)
A 3 2 4
B 1 4 2
C 5 none 3.5
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 solve the problem using Microsoft Excel Solver. For the formulation, provide a complete description of the decision variables used along with their units and also label the constraints mentioned in the problem as completely as possible. Also, the Excel set-up should provide clearly labeled values used for the decision variables, constraints, and objective function.