Burger Office Equipment produces two types of desks, standard and deluxe. Deluxe
ID: 3175468 • Letter: B
Question
Burger Office Equipment produces two types of desks, standard and deluxe. Deluxe desks have oak tops and more-expensive hardware and require additional time for finishing and polishing.standard desks require 80 square feet of pine and 12 hours of labor,while deluxe desks require 62 square feet of pine,18 square feet of oak,and 18 hours of labor.for the next week,the company has 5000 square feet of pine,700 square feet of oak,and 400 hours of labor available.standard desks net a profit of $75,while deluxe desks net a profit of $160.all desks can be sold to national chains such as staples or office depot.a)develop a linear optimization model to determine how many of each the company should make next week to maximize profit contribution.b)implement your model on a spreadsheet and find an optimal solution.c)explain the reduced cost associated with standard desks.d)what constarints are binding?explain how the shadow price can be used to make decisions that will improve profitability. e)if 25% of the oak is deemed to be cosmetically defective,how will the optiomal solution be affected? F)the shop foreman is suggesting that his workforce be allowed to work an additional 100 hours at an overtime premium of $ 6/hour.is this a good suggestion?why or hy not?
Explanation / Answer
Solution:-
a&b :::
Solution:
Part a &b
Decision Variables
No of standard desk X = 0
No of Deluxe desk Y= 22
Constrain
Amount of pine for next week 5000
Amount of Oak for next week 700
amount of labor hours 400
Payoff table X Y Total Constrain
Pine Reqd 80 62 1364 < 5000
Oak reqd 0 18 396 < 700
labor reqd 12 18 396 < 400
Objective function
75*X + 160 *y
= $ 3520.0
Optimal solution for base case is
No of standard desk X = 0
No of Deluxe desk Y= 22
Maximum Proft = $ 3520.0
c&d ::
Decision Variables No of standard desk X = 33 No of Deluxe desk Y= 0 Constrain Amount of pine for next week 5000 Amount of Oak for next week 700 amount of labor hours 400 Payoff table X Y Total Constrain Pine Reqd 80 62 2640 < 5000 Oak reqd 0 18 0 < 700 labor reqd 12 18 396 < 400 Objective function (75+31.66)*X + 160 *y = $ 3521.1 Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $E$20 X = 0 -31.6667 75 31.66667 1E+30 Rreduced cost is 31.66667 So if the coeffof objective function of X is increased by $ 31.66 then the optimal solution of x will be positive Part d: Only labor requirement is a binding constrain. Part d : shadow price is the increase in profit or objective function possible with every unit increase in binding constrain. so every unit increase in labor hours will result in $8.88 increase in profit. Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $G$29 Pine Reqd Total 1377.778 0 5000 1E+30 3622.222 $G$30 Oak reqd Total 400 0 700 1E+30 300 $G$31 labor reqd Total 400 8.888889 400 300 400Related Questions
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