Question

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	5
2	5	4
3	5	2

The shaper is available for 110 hours, and the grinder is available for 100 hours. No more than 190 units of component 3 can be sold, but up to 1075 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 $7, $6, and $9, respectively.

1. Formulate and solve for the recommended production quantities.
   

   	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	6C1	+	___C2	+	___C3	≤	____	Constraint 1
   	___C1	+	___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	=
   C2	=
   C3	=

2. 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 two decimal places.
   

   	Objective Coefficient Range
   Variable	lower limit	upper limit
   C1
   C2
   C3

   
   Interpret the above ranges for company management.
   
   The input in the box below will not be graded, but may be reviewed and considered by your instructor.
   
   
   
3. 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 two decimal places.
   

   	Right-Hand-Side-Range
   Constraints	lower limit	upper limit
   1
   2
   3
   4
   5
   6

   
   Interpret the above ranges for company management.
   
   
   
4. If more time could be made available on the grinder, how much would it be worth?
   
   
   
5. If more units of component 3 can be sold by reducing the sales price by $4, should the company reduce the price? Yes or no.
   
   

Answer 1

a)

b) Using Excel solver link excel file: https://1drv.ms/x/s!AkW5WQDSTr7DhxEjSfCca859fcMK

	C1	C2	C3
	600	410	190
Profit	$       7.00	$       6.00	$       9.00
Max Z =	8370
S.T.					LHS		RHS
Shaper	6	5	5		6600	<=	6600
Grinder	5	4	2		5020	<=	6000
C3			1		190	<=	190
C1	1				600	<=	1075
C2		1			410	<=	475
C1	1				600	>=	600

C1	=	600
C2	=	410
C3	=	190

Microsoft Excel 16.0 Sensitivity Report
Worksheet: [Book1]Sheet1
Report Created: 3/2/2020 11:58:10 PM
Variable Cells
			Final	Reduced	Objective	Allowable	Allowable
	Cell	Name	Value	Cost	Coefficient	Increase	Decrease
	$B$2	C1	600	0	7	0.2	1E+30
	$C$2	C2	410	0	6	3	0.166666667
	$D$2	C3	190	0	9	1E+30	3
Constraints
			Final	Shadow	Constraint	Allowable	Allowable
	Cell	Name	Value	Price	R.H. Side	Increase	Decrease
	$F$13	C1 LHS	600	-0.2	600	341.6666667	54.16666667
	$F$8	Shaper LHS	6600	1.2	6600	325	2050
	$F$9	Grinder LHS	5020	0	6000	1E+30	980
	$F$10	C3 LHS	190	3	190	410	65
	$F$11	C1 LHS	600	0	1075	1E+30	475
	$F$12	C2 LHS	410	0	475	1E+30	65

b)
Objective Coefficient Range
Variable	lower limit	upper limit
C1	NA	$    7.20
C2	$     5.83	$    9.00
C3	$     6.00	NA

c)
Right-Hand-Side-Range
Constraints	lower limit	upper limit
1	4550	6925
2	5020	NA
3	125	600
4	600	NA
5	410	NA
6	545.8333	941.666667

d)

more time available = 6925 - 6600 = 325 minutes = 6 hour 25 minutes.

e)

No we can not increase sales by the model redicing 4$ profit of C3