Vollmer Manufacturing makes three components for sale to
refrigeration companies. The components are processed on two
machines: a shaper and a grinder. The times (in minutes) required
on each machine are as follows:
Machine |
Component |
Shaper |
Grinder |
1 |
6 |
4 |
2 |
4 |
5 |
3 |
4 |
2 |
The shaper is available for 120 hours, and the grinder for 110
hours. No more than 200 units of component 3 can be sold, but up to
1,000 units of each of the other components can be sold. In fact,
the company already has orders for 600 units of component 1 that
must be satisfied. The profit contributions for components 1, 2,
and 3 are $8, $6, and $9, respectively.
(a) |
Formulate and solve for the recommended production quantities.
If the constant is "1" it must be entered in the box. If an amount
is zero, enter "0". |
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Let C1 |
= units of component 1 manufactured |
C2 |
= units of component 2 manufactured |
C3 |
= units of component 3 manufactured |
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Max |
C1 |
+ |
C2 |
+ |
C3 |
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s.t. |
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C1 |
+ |
C2 |
+ |
C3 |
- Select your answer -≤≥=Item 7 |
|
Shaper |
|
C1 |
+ |
C2 |
+ |
C3 |
- Select your answer -≤≥=Item 12 |
|
Grinder |
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C3 |
- Select your answer -≤≥=Item 15 |
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Maximum units of component 3 |
|
C1 |
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- Select your answer -≤≥=Item 18 |
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Maximum units of component 1 |
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C2 |
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- Select your answer -≤≥=Item 21 |
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Maximum units of component 2 |
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C1 |
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- Select your answer -≤≥=Item 24 |
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Minimum units of component 1 |
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C1, C2,
C3 |
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- Select your answer -≤≥=Item 26 |
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Optimal solution: C1 = ,
C2 = , C3= |
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(b) |
What are the objective coefficients ranges for the three
components? If required, round your answers to two decimal
places. |
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Variable |
Objective Coefficient Range |
C1 |
- Select your answer -No Lower Limit7.335.466.00Item 31 to -
Select your answer -No Upper Limit9.008.569.50Item 32 |
C2 |
- Select your answer -No Lower Limit4.335.336.00Item 33 to -
Select your answer -No Upper Limit9.008.5610.00Item 34 |
C3 |
- Select your answer -No Lower Limit5.005.506.00Item 35 to -
Select your answer -No Upper Limit10.009.509.00Item 36 |
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Interpret these ranges for company management. |
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The input in the box below will not be graded, but may be
reviewed and considered by your instructor. |
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(c) |
What are the right-hand-side ranges? |
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Constraint |
Right-Hand-Side Range |
1 |
- Select your answer -No Lower Limit430044004500Item 38 to -
Select your answer -No Upper Limit744075007550Item 39 |
2 |
- Select your answer -No Lower Limit433053306300Item 40 to -
Select your answer -No Upper Limit850072006600Item 41 |
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Interpret these ranges for company management. |
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The input in the box below will not be graded, but may be
reviewed and considered by your instructor. |
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(d) |
If more time could be made available on the grinder, how much
would it be worth? |
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- Select your answer -Profit of $1000Profit of $200NothingItem
43 |
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Explain. |
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The input in the box below will not be graded, but may be
reviewed and considered by your instructor. |
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(e) |
If more units of component 3 can be sold by reducing the sales
price by $4, should the company reduce the price? |
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- Select your answer -YesNoItem 45 |
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Explain. |
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The input in the box below will not be graded, but may be
reviewed and considered by your instructor. |
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Please show how to solve using excel if possible, thanks.
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