The shaper is available for 125 hours, and the grinder is available for 95 hours
ID: 397590 • Letter: T
Question
The shaper is available for 125 hours, and the grinder is available for 95 hours. No more than 170 units of component 3 can be sold, but up to 1050 units of each of the other components can be sold. In fact, the company already has orders for 625 units of component 1 that must be satisfied. The profit contributions for components 1, 2, and 3 are $8, $6, and $9, respectively. Formulate and solve for the recommended production quantities. If the constant is "1" it must be entered in the box. Let C1 = units of component 1 manufactured C2 = units of component 2 manufactured C3 = units of component 3 manufactured Max 8 C1 + 6 C2 + 9 C3 s.t 7C1 + 5 C2 + 5 C3 Constraint 1 5 C1 + 5 C2 + 2C3 Constraint 2 C3 Constraint 3 C1 Constraint 4 C2 Constraint 5 C1 Constraint 6 C1,C2,C3 0 The optimal solution is C1 = 600 C2 = 700 C3 = 200 Profit = $ What are the objective coefficient ranges for the three components? If there is no lower or upper limit, then enter the text "NA" as your answer. If required, round your answers to one decimal place. Enter "0" if your answer is zero. Objective Coefficient Range Variable lower limit upper limit C1 5.1 9 C2 4.7 8.2 C3 3.2 1E+30 Interpret the above ranges for company management. As long as the profit contribution of component 1 is between $ and $ then the optimal solution will not change. As long as the profit contribution of component 2 is between $ and $ then the optimal solution will not change. As long as the profit contribution of component 3 is more than $ then the optimal solution will not change. The assumption is that only variable(s) will change at a time. What are the right-hand-side ranges? If there is no lower or upper limit, then enter the text "NA" as your answer. If required, round your answers to the nearest whole number. If your answer is zero, enter "0". Right-Hand-Side-Range Constraints lower limit upper limit 1 2 3 4 5 6 Interpret the above ranges for company management. The right-hand-side ranges are the ranges over which the for the associated constraints are applicable. If more time could be made available on the grinder, how much would it be worth? If required, round your answers to two decimal places. $ , since the dual value is on the grinder at the optimal solution. If more units of component 3 can be sold by reducing the sales price by $4, should the company reduce the price? , since at that price it be profitable to produce any of component 3.
Explanation / Answer
As per given data:
Max 8 C1 + 6 C2 + 9 C3
s.t
7C1 + 5 C2 + 5 C3 7500 Constraint 1 (time available in minutes at shaper)
5 C1 + 5 C2 + 2C3 5700 Constraint 2 (time available in minutes at grinder)
C3 170 Constraint 3 (not more than 170 units)
C1 1050 Constraint 4 (not more than 1050 units)
C2 1050 Constraint 5 (not more than 1050 units)
C1 625 Constraint 6 (order of 625 units)
C1,C2,C3 0 Non-negativity constraint
The optimal solution is
C1 = 600 C2 = 700 C3 = 200
Profit = $8(600) + $6(700) + $9(200) = $10,800
Profit = $10,800
What are the objective coefficient ranges for the three components? Objective Coefficient Range Variable lower limit upper limit C1 5.1 9 C2 4.7 8.2 C3 3.2 1E+30 Interpret the above ranges for company management.
As long as the profit contribution of component 1 is between $5.1 and $9 then the optimal solution will not change.
As long as the profit contribution of component 2 is between $4.7 and $8.2 then the optimal solution will not change.
As long as the profit contribution of component 3 is more than $3.2 then the optimal solution will not change.
The assumption is that only single variable(s) will change at a time.
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