Super Door Inc. manufactures and sells 3 standard doors: simple door (D1), double door (D2), and patio door (D3). The demand for doors is seasonal and Super Door does not have enough capacity or flexibility to satisfy the demand for summer sales on a just-in-time basis. To overcome this problem, Super Door manufactures some doors during the winter and stores them in a warehouse near the plant. 

The maximum storage capacity of the warehouse is 25,000 cubic feet, and the storage costs are estimated to be 8% of the average contribution margin. During the manufacturing process, each door must go through an assembling workshop. The capacities in both summer and winter for the assembling workshop are 2,000 hours for the summer and 2,000 hours for the winter. 

During the manufacturing process, each door must go through a packing workshop. The capacities in both summer and winter for the packing workshop are 500 hours for the summer and 500 hours for the winter. Power Door has only 1 customer, which is an association of many small hardware stores. At the beginning of each winter, the association informs Power Door of the maximum number of units of each door the association will buy in summer. 

The maximum demand, the average contribution margin, and the requirements for storage, assembling, and packing are as follows: Estimated Maximum Storage Assembling Packing Demand for Contribution Requirements Requirements Requirements Doors Each Door (in Units) Margin per Unit (in Cubic Feet) (in Hours) (in Hours) D1 2,500 $150 12 1.0 0.2 D2 900 250 20 1.5 0.4 D3 750 300 24 2.0 0.4 

The controller of Power Door Inc. has set up the following linear program to maximize the contribution margin of the year: Maximize contribution margin in $/year: CM (D1S, D2S, D3S, D1W, D2W, D3W) = 150D1S + 250D2S + 300D3S + 138D1W + 230D2W+ 276D3W Subject to: D1S+ D1W<= 2500 maximum demand for D1/year D2S+ D2W<= 900 maximum demand for D2/year D3S+ D3W<= 750 maximum demand for D3/year 12D1W+ 20D2W+ 24D3W<= 25000 maximum storage capacity/year 1D1S + 1.5D2S + 2D3S<= 2000 maximum assembly capacities/summer 1D1W + 1.5D2W + 2D3W<= 2000 maximum assembly capacities/winter 0.2D1S + 0.4D2S + 0.4D3S<= 500 maximum packing capacities/summer 0.2D1W + 0.4D2W + 0.4D3W<= 500 maximum packing capacities/winter D1S, D2S, D3S, D1W, D2W, D3W >= 0 Where: D1S represents the number of simple doors (D1) produced during the summer (S) D2S represents the number of double doors (D2) produced during the summer (S) D3S represents the number of patio doors (D3) produced during the summer (S) D1W represents the number of simple doors (D1) produced during the winter (W) D2W represents the number of double doors (D2) produced during the winter (W) D3W represents the number of patio doors (D3) produced during the winter (W).

REQUIRED 

1. Formulate and solve the linear programming problem to determine the product mix that will maximize the total contribution margin for the year for Super Door Inc. 

2. Based on the report, how many packing hours are not used during the year? Briefly explain. 

3. Based on the reports, how much should Super Door be willing to pay for additional storage capacity? Briefly explain. 

4. What is the total contribution margin associated with the units produced during the winter? Show all your calculations.