2. Joyce Lumber Company umber both require a certain produces tables and chairs.

Question

2. Joyce Lumber Company umber both require a certain produces tables and chairs. The production process for each is similar in that the painting number of labor hours in he Each chair department Each table r takes three hours of work hours of painting work. hours of carpentry four of and one hour of During the 2A00 e company time and 1.000 hours available. department wants to make no more than pa this month because of available new chairs ause the existing nventory of tables is low, the marketi department wants the each chair sold least 100 tables this month. Each table sold makes a profit contribution of ST and makes profit of problem is to determine the best possible The maximum profit. combination and to manufacture this month in order to attain the would like to solve this as a linear programming probl Use the information below to answer the following questions Joyce Lumber Co. Tables Chairs 320 360 Units 5 4040 Profits Constraints 2400 4 2400 Carpentry 1000 Painting Max Chairs Min Table a What is the optimal production solution to this problem? What is the total profit? b) What are the allowable numbers of chairs and tables that can be produced before the optimal solution c) What is the impact on profits of a decrease in painting time of 100 hours? Does the optimal solution change? solution d) What is the impact on profits of an increase in carpentry time of 200 hours? Does the optimal change? increases e) Will the optimal solution change if the market price is able to increase and the profit per chair by S4?

Explanation / Answer

a) optimal production solution is 320 tables and 360 chairs. Total profit = 320*7 + 360*5 = $4040

b) Minimum number of tables <=320 and max number of chairs >= 360.

The Shadow Price corresponds to the exchange rate of the Linear Programming model’s optimal value compared to the marginal modification of the right hand side (RHS) of the constraint.

c) Using above, the shadow price for painting time is 2.6 and the decrease is within allowable ranges.

Thus, decreasing it by 100 hours means our new optimal profit will be decreased by $100*2.6

Thus new optimal profit = $4040 - $100*2.6 = $3780

d) Similarly, the shadow price for carpentry time is 0.6 and the increase is within allowable ranges.

Thus, increasing it by 200 hours means our new optimal profit will be increased by $200*0.6

Thus, new optimal profit = $4040 + $200*0.6 = $4160

e) From the variable cells, we can see that the allowable increase for the coefficient of chairs is 4.333.

Thus an increase of $4 won't change the optimal solution.

DO THUMBS UP ^_^

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