Question 3: The Dakota Furniture Company manufactures desks, tables, and chairs

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Question 3: The Dakota Furniture Company manufactures desks, tables, and chairs The manufacture of each type of furniture requires lumber and two types of skilled la- bor: finishing and carpentry. The amount of each resource needed to make each type of furniture is given in the following table: Desk Table Chair 86 Resource Lumber (board ft Finishing hours Carpentry hours 4 1.5 0.5 Currently, 48 board feet of lumber, 20 finishing hours, and 8 carpentry hours are available per week. A desk sells for $60, a table for $30, and a chair for $20. Dakota wants to maximize the total revenue. a) Formulate this problem as an LP and find the optimal solution b) Find the dual prices for the resources from the optimal tableau c) Calculate the ranges for the changes in the right hand side vector such that the basis still remains feasible d) Calculate the ranges for the changes of the objective coefficients such that the basis still remains feasible

Explanation / Answer

Question 3: The Dakota Furniture Company manufactures desks, tables, and chairs The manufacture of each type of furniture requires lumber and two types of skilled la- bor: finishing and carpentry. The amount of each resource needed to make each type of furniture is given in the following table: Desk Table Chair 86 Resource Lumber (board ft Finishing hours Carpentry hours 4 1.5 0.5 Currently, 48 board feet of lumber, 20 finishing hours, and 8 carpentry hours are available per week. A desk sells for $60, a table for $30, and a chair for $20. Dakota wants to maximize the total revenue. a) Formulate this problem as an LP and find the optimal solution b) Find the dual prices for the resources from the optimal tableau c) Calculate the ranges for the changes in the right hand side vector such that the basis still remains feasible d) Calculate the ranges for the changes of the objective coefficients such that the basis still remains feasible

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