I need detailed solution about this. (Operation research 1) 7. (12 points) A com

Question

I need detailed solution about this. (Operation research 1)

7. (12 points) A company produces and sells chairs and desks. Each chair requires 3 board feet of lumber and 2 hours of labor. Each desk requires 5 board feet of lumber and 4 hours of labor. A total of 145 board feet of lumber and 90 hours of labor are availble. Upto 50 chairsrs and 50 desks can be sold. Chairs sell for $55, and desks for $32. In addition to producing chairs and desks itself, the company can buy (from an outside supplier) extra chairs at $27 each and extra desks at $50 each. Let CM, DM be the number of chairs and desks made by the company, and CB, DB the number of chairrs and desks bought from the supplier. Use the Lindo output below to answer each of the following parts. 32CM +55DM +5CB+5DB 3CM+5DM 2CM +4DM max S 145 90 S 50 S 50 3) 4) 5) objective function value 1715.00000 variable CM DM CB DB row slack or surplus dual prices 2) 3) 4) 5) CM +CB DM +DEB value reduced cost 45.000000 1.000000 5.000000 50.000000 0.000000 13.500000 5.000000 5.000000 10.000000 Range in which basis remains unchanged: OBJ coefficient ranges variable current coef allowable increase allowable decrease CM DM 55.000000 CB DB infinity 4.00000 2.00000 infinity 2.00000 infinity 5.00000 4.00000 32.000000 5.00000 5.00000 righthand side ranges row current RHS allowable increase allowable decrease infinity 6.66667 infinity 2 145.00000 90.00000 50.00000 5 50.00000 10.000000 90.00000 5.00000 50.00000 3

Explanation / Answer

a) Profit from DB increases from 5 to 7 because 5 Profit was earlier when we were buying at 50$ now buying at 48$ will reduce the buying cost by 2 units.

So, hence Profit from DB increases with 2 units which is an allowable increase Hence BFS is optimal.

Z = 1715 + 2 * (50) = 1815. (50 - earlier cost of desk)

b)

0 is the ans as in the question it is mentioned that we can't  give dual price of the lumber.

c)

Maximum 50 desks can be sold.

Decrease is 10 units which is less than 50 so, allowable desks can be sold.

Hence ofcourse, loss is there so it will be less than optimum solution

Let me calculate new BFS,

Z = 1715 - 10(5) = 1715- 50 = 1665 ( 10 - decrease)

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