1) Swearingen and McDonald, a small furniture manufacturer, produces fine hardwood tables and chairs. Each product must go through three stages of the manufacturing process: assembly, finishing, and inspection. Each table requires 12 hours of assembly, 20 hours of finishing, and 2 hours of inspection. Each chair requires 4 hours of assembly, 16 hours of finishing, and 3 hours of inspection. The profit per table is $150 while the profit per chair is $100. Currently, each week there are 300 hours of assembly time available, 220 hours of finishing time, and 30 hours of inspection time. To keep a balance, the number of chairs produced should be at least twice the number of tables. Also, the number of chairs cannot exceed 6 times the number of tables. (You may use QM-software for this problem. All the detailed output should be displayed).

a)     Formulate this as a linear programming problem. Carefully define all decision variables.

b)    Show the graph of the feasible region indicating all the relevant corner points

c)     Find the optimal solution to this LP and find the maximum profits.

 

Decision variables are factors in your model that you can control, for example, how much lease to charge or how much cash to put resources into a shared asset. Choice factors aren't needed for Crystal Ball models, yet are needed for OptQuest models. You characterize choice factors in Crystal Ball by tapping the Define Decision button in the Crystal Ball strip. 

At the point when you characterize a choice variable in Crystal Ball, you characterize its: 

Limits—Defines the upper and lower limits for the variable. OptQuest looks for answers for the choice variable just inside these cutoff points. 

Type—Defines whether the variable sort is discrete, constant, double, classification, or custom: 

Nonstop — A variable that can be partial (that is, it isn't needed to be a whole number and can take on any incentive between its lower and upper limits; no progression size is required and any given reach contains an endless number of potential qualities. 

Step-by-step explanation

Discrete — A variable that can just accept values equivalent to its lower bound in addition to a different of its progression size; a stage size is any number more noteworthy than zero yet not exactly the variable's reach. 

Parallel — A choice variable that can be is 0 or 1 to speak to a yes-no choice, where 0 = no and 1 = yes. 

Classification — A choice variable for speaking to ascribes and records; can accept any discrete number between the lower and upper limits (comprehensive), where the request (or heading) of the qualities doesn't make a difference (ostensible). The limits must be numbers. 

Custom — A choice variable that can expect any an incentive from a rundown of explicit qualities (two qualities or more). You can enter a rundown of qualities or a cell reference to a rundown of qualities in the bookkeeping page. In the event that a cell reference is utilized, it must incorporate more than one cell so there will be at least two qualities. Spaces and non-numeric qualities in the reach are overlooked. In the event that you enter values in top notch, they should be isolated by a substantial rundown separator - a comma, semicolon, or other worth determined in the Windows local and language settings.