Question

The Wyndor Corporation is in the business of manufacturing windows and doors. They have identified unused capacity in three of their manufacturing plants that they would like to take advantage of through the introduction of two new products: an eight-foot aluminum storm door and a three-foot by two-foot wooden double-hung window. Their only objective in doing so is to increase profits from the business as much as possible. Their accounting department has estimated that the gross margin of selling doors is $4,500 per unit and the gross margin for selling windows is $6,000 per unit. The company can make as many as they wish with these returns. Each door requires one unit of capacity from the Aluminum Frames Plant and three units of capacity from the Glass and Assembly Plant. Each window requires two units of capacity from the Wood Frames plant and two units of capacity from the Glass and Assembly Plant. The Aluminum Frames plant currently has five units of available capacity, Wood Frames has fourteen units and Glass and Assembly has twenty units.

1a. What is your objective function? Be sure to include the equation of your objective function. (3 pts)

b. What are your decision variables? (3 pts

c. What are your constraints and RHS variables? (4 pts)

Answer 1

1a. let 'V' be the profit of the firm.

so the objective is : max V = 4500x + 6000y ; where x is the total units of doors and y is the total units of windows.

1b. Here the decision variables are x and y, becuase the company has to choose between producing different combinations of x and y.

1c. Here the constraint to the firm is the cost constraint:

Let C be the total cost borne by the firm in the production of x and y, and P_x and P_y be the cost of producing one unit of x and y respectively.

so the cost constraint is C = P_x.x + P_y.y ; where the RHS is the aggregate spending of the firm to produce doors and windows.