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What are the objective coefficients ranges for the three components? If required, round your answers to two decimal places.

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Learning Goal: I’m working on a accounting question and need an explanation and answer to help me learn.

correct answers

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 120 units of component 3 can be sold, but up to 1,000 units of component 1 and up to 600 units of component 2 can be sold. In fact, the company already has orders for 600 units of component 1 that must be satisfied. The per unit selling price and per unit variable costs for each of the three components are as follows:

Component Selling price Material Cost Labor Cost
1 $25 $12 $5
2 $18 $8 $4
3 $27 $13 $5
(a) For each component, calculate the profit margin (profit margin = selling price – material cost – labor cost).
Component 1: $ 
Component 2: $ 
Component 3: $ 
Formulate and solve the model to determine the maximum profit. If the constant is “1”, it must be entered in the box. If an amount is zero, enter “0”.
Let C1 = units of component 1 manufactured
C2 = units of component 2 manufactured
C3 = units of component 3 manufactured
Max $ C1 + $ C2 + $ C3
s.t.
 C1 +  C2 +  C3 – Select your answer –
≤
≥
= 		Shaper
 C1 +  C2 +  C3 – Select your answer –
≤
≥
= 		Grinder
 C3 – Select your answer –
≤
≥
= 		Maximum units of component 3
 C1 – Select your answer –
≤
≥
= 		Maximum units of component 1
 C2 – Select your answer –
≤
≥
= 		Maximum units of component 2
 C1 – Select your answer –
≤
≥
= 		Minimum units of component 1
C1, C2, C3 – Select your answer –
≤
≥
=
Maximum profit: $
(b) What are the objective coefficients ranges for the three components? If required, round your answers to two decimal places.
Variable Objective Coefficient Range
C1 – Select your answer –
No Lower Limit
0.00
3.67
5.33
 to 
– Select your answer –
No Upper Limit
6.67
9.00
10.00
C2 – Select your answer –
No Lower Limit
2.67
3.67
5.33
 to 
– Select your answer –
No Upper Limit
6.67
8.00
9.00
C3 – Select your answer –
No Lower Limit
2.67
4.17
5.33
 to 
– Select your answer –
No Upper Limit
6.33
9.00
10.00
Interpret these ranges for company management.
Individual changes in the profit coefficients 
– Select your answer –
within
outside
 these ranges will not cause a change in the optimal number of components to produce.
(c) What are the right-hand-side ranges?
Constraint Right-Hand-Side Range
1 – Select your answer –
No Lower Limit
6,380
6,480
6,580
 to 
– Select your answer –
No Upper Limit
7,920
8,000
8,050
2 – Select your answer –
No Lower Limit
6,120
6,210
6,410
 to 
– Select your answer –
No Upper Limit
6,600
7,200
8,680
Interpret these ranges for company management.
These are the ranges over which the shadow prices for the associated constraints 
– Select your answer –
are
are not
 applicable.
(d) If more time could be made available on the grinder, how much would it be worth? Explain.
– Select your answer –
It would be worth nothing
The worth depends on the extra time available
 , because the constraint related to the time available on the grinder 
– Select your answer –
is
is not
 binding.
(e) If more units of component 3 can be sold by reducing the sales price by $4, should the company reduce the price?
– Select your answer –
Yes
No
, because the production of component 3 would be 
– Select your answer –
less
still more
 profitable than the production of the other two components and at the reduced price 
– Select your answer –
none
more units
 of component 3 would be produced.
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