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Solve using your computer -Answer Questions a to l below:

 

Consider a furniture company that produces sofa, chairs and tables at its plant in Dammam Industrial district. The company’s management set a requirement to produce at least twice the number of chairs as the number of sofas. The plant uses three main resources to make the furniture: wood, cloth, and labor. The resource requirements for each piece of furniture and the total resource available weekly are as listed below:

 

Furniture                                             Resource requirement

Product                       Wood (Ib.)                  Cloth (yards)               Labor (hours) 

Sofa                                         7                                  12                                6

Chair                                       4                                  7                                  5

Table                                       5                                  -                                   9

Total Available

Resource                                 2,250                           1,000                           240

 

The company produces the furniture on a weekly basis and use a warehouse that has a total capacity of 650 pieces of furniture. Each sofa earns $400 in profit, each chair $190, and each table $275. The company wants to know how many pieces of each type of furniture to make per week to maximize profit. The linear programming model for this problem is as listed below:

 

Let       X1 = number of Sofas to produce weekly

            X2 = number of chairs to produce weekly

            X3 = number of tables to produce weekly

 

                        Max                 400 X1            + 190 X2 + 275 X3

 

                        Subject to        X2 > 2X1                    or       2X1 – X2          < 0

                                                X1 +X2 + X3                                                  < 650

                                                7X1 + 4X2 + 5X3                                           < 2250

                                                12X1 + 7X2                                                    < 1000

                                                6X1 + 5X2 + 9X3                                           < 240

                                                 X1, X2, X3                                                    > 0

 

Report the optimal answer as obtained by using Solver and/or Solver-Table:

 

 

a)         X1 = ______,              X2 = ______, X3 = ________, Profit = ______.       (5 points)

 

b)         Range of optimality for the Sofa Profit:                                                         (2 points)

 

 

c)         Range of optimality for the chair Profit:                                                        (2 points)

 

 

 d)        Range of optimality for the table Profit:                                                        (2 points)

 

 

Questions (e to f) @ 1 point each (9 points):

 

e)         Assuming the cost of storage is a sunk cost, how much would the company be willing to pay for an additional unit of space in the warehouse?                            

 

 

 

f)         How many additional storage units would you recommended to buy?          

 

 

 

g)         Assuming the cost of wood is included in computing the profits as $2.00/Ib., how much would the company be willing to pay for an additional lb. of wood?    

 

 

h)         How many additional pounds of wood would you recommend to buy?      

 

 

i)          Assuming the cost of cloths is included in computing the profits as $1.00/yard, how much would the company be willing to pay for additional yards of cloth?     

 

 

j)          How many additional yards of cloths would you recommend to buy?       

 

k)         Assuming the cost of labor hours is a sunk cost, how much would the company be willing to pay for an additional hour of labor time?              

 

 

 

l)          How many additional labor hours would you recommend to buy?