Mark has a company that produces tables and chairs, both having two different models. The product models and related information are given in the following table. Wood costs 3000 $ per cubic meter and 200 m3 of wood are available for the upcoming month. The cost of labor is 40 $/hour and there are 6000 hours of labor available in a month. Mark sells his products to a big chain retail company. The company purchases all products whatever Mark produces. Mark formulates an LP as follows to determine the optimal monthly production plan such that he maximizes the total profit. Decision Variables: X1 : number of basic tables to be produced. X2 : number of elegant tables to be produced. X3 : number of basic chairs to be produced. X4 :number of elegant chairs to be produced. Max Z = 140 X1 + 345 X2 + 120 X3 + 260 X4 ( maximize total profit) Subject to 0.11 X1 + 0.13 X2 + 0.06 X3 + 0.07 X4 ≤ 200 (constraint on the available amount of wood) 2 X1 + 4.5 X2 + 1.5 X3 + 4 X4 ≤ 6000 (constraint on the available amount of labor hours) Mark has run that model and found the optimal solution of the problem as follows. a) Another customer requests to buy 250 elegant chairs with the price of 660 $ each. Notice that the current selling price of elegant chair is 630 $ each. Should Mark accept or decline the offer? Why? Explain your answer by referring the terms in standard and sensitivity analysis, i.e. dual price, reduced cost, allowable increase/decrease etc. Assume that the available amounts of labor hours and wood remains constant and the retail company does not object to that deal if Mark accepts. b) Mark considers to hire one or two more employees to increase his production and hence his profit. However he doesn’t want to change the current production plan (doesn’t want to change the basis) One additional employee adds 40 hours/month to the labor resource. Should Mark hire new employee(s)? If not, why? If yes, how many and why? Explain your answer by referring the terms in standard and sensitivity analysis, i.e. dual price, reduced cost, allowable increase/decrease etc. c) Because of the sickness and some other reasons, some days, employees arrive late to the factory or don’t show up that day. Therefore some loss in labor resource is observed. How much total loss should Mark tolerate in labor hours without changing the current production plan (without changing the basis)? Explain your answer by referring the terms in standard and sensitivity analysis, i.e. dual price, reduced cost, allowable increase/decrease etc.
Mark has a company that produces tables and chairs, both having two different models. The product models and related information are given in the following table.
Wood costs 3000 $ per cubic meter and 200 m3 of wood are available for the upcoming month. The cost of labor is 40 $/hour and there are 6000 hours of labor available in a month. Mark sells his products to a big chain retail company. The company purchases all products whatever Mark produces.
Mark formulates an LP as follows to determine the optimal monthly production plan such that he maximizes the total profit.
Decision Variables:
X1 : number of basic tables to be produced.
X2 : number of elegant tables to be produced.
X3 : number of basic chairs to be produced.
X4 :number of elegant chairs to be produced.
Max Z = 140 X1 + 345 X2 + 120 X3 + 260 X4 ( maximize total profit)
Subject to
0.11 X1 + 0.13 X2 + 0.06 X3 + 0.07 X4 ≤ 200 (constraint on the available amount of wood)
2 X1 + 4.5 X2 + 1.5 X3 + 4 X4 ≤ 6000 (constraint on the available amount of labor hours)
Mark has run that model and found the optimal solution of the problem as follows.
a) Another customer requests to buy 250 elegant chairs with the price of 660 $ each. Notice that the current selling price of elegant chair is 630 $ each.
Should Mark accept or decline the offer? Why? Explain your answer by referring the terms in standard and sensitivity analysis, i.e. dual price, reduced cost, allowable increase/decrease etc.
Assume that the available amounts of labor hours and wood remains constant and the retail company does not object to that deal if Mark accepts.
b) Mark considers to hire one or two more employees to increase his production and hence his profit. However he doesn’t want to change the current production plan (doesn’t want to change the basis) One additional employee adds 40 hours/month to the labor resource.
Should Mark hire new employee(s)? If not, why? If yes, how many and why?
Explain your answer by referring the terms in standard and sensitivity analysis, i.e. dual price, reduced cost, allowable increase/decrease etc.
c) Because of the sickness and some other reasons, some days, employees arrive late to the factory or don’t show up that day. Therefore some loss in labor resource is observed.
How much total loss should Mark tolerate in labor hours without changing the current production plan (without changing the basis)?
Explain your answer by referring the terms in standard and sensitivity analysis, i.e. dual price, reduced cost, allowable increase/decrease etc.
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