Question

Need A-D

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".

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 Shaper

C1 + C2 + C3 Grinder

C3 Maximum units of component 3

C1 Maximum units of component 1

C2 Maximum units of component 2

C1 Minimum units of component 1

C1, C2, C3

Optimal solution: C1 = , C2 = , C3=

(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 to

C2 to

C3 to

Interpret these ranges for company management.

The input in the box below will not be graded, but may be reviewed and considered by your instructor.

(c) What are the right-hand-side ranges?

Constraint Right-Hand-Side Range

1 to

2 to

Interpret these ranges for company management.

The input in the box below will not be graded, but may be reviewed and considered by your instructor.

(d) If more time could be made available on the grinder, how much would it be worth?

Explain.

The input in the box below will not be graded, but may be reviewed and considered by your instructor.

(e) If more units of component 3 can be sold by reducing the sales price by $4, should the company reduce the price?

Explain.

The input in the box below will not be graded, but may be reviewed and considered by your instructor.

Answer 1

SOLUTION

	Machine (time in Min)				Profit per unit
Component	Shaper	Grinder	Min Units	Max Units
1	6	4	600	1000	$8
2	4	5		1000	$6
3	4	2		200	$9
Total time (Hr)	120	110
Total time (Min)	7200	6600

Let C1 be the number of component 1 manufactured

C2 be the number of component 2 manufactured

C3 be the number of component 3 manufactured

So obejective function will be MAximise Z = 8C1 +6C2+9C3

Constraints:

Avaialbity of Hours of machine

6C1+4C2+4C3<=7200 ...For Shaper

4C1+5C2+2C3<=6600 ...For grinder

Component 1 has order of 600 and must be satisfied

Therefore C1>=600

No more than 200 units of component 3 can be sold

Therefore C3<=200

Upto 1000 units of component 1 and 2 can be sold

Therefore C1<=1000

C2<=1000

C1,C2,C3>=0 (Non negative)

So our LPP is

MAximise Z = 8C1 +6C2+9C3

Subject to

6C1+4C2+4C3<=7200

4C1+5C2+2C3<=6600

C1>=600

C3<=200

C1<=1000

C2<=1000

C1,C2,C3 >=0

Solution C1= 600 units

C2= 700 units

C3= 200 units

Adjustable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $E$14 Var C1 600 0 8 1 1E+30 $F$14 Var C2 700 0 6 3 0.666666667 $G$14 Var C3 200 0 9 1E+30 3 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $G$19 C3 7200 1.5 7200 240 2800 $G$21 C3 6300 0 6600 1E+30 300 $G$24 C3 600 -1 600 400 85.71428571 $G$27 C3 200 3 200 700 100 $G$30 C3 600 0 1000 1E+30 400 $G$32 C3 700 0 1000 1E+30 300

Range is allowabe increase and allowable decrease

For C1, range is NA to 9 (8+1)

For C2, Range is 6 (6-0.667) to 9 (6+3) (5.33 not possible as C1 should be integer)

For C3, range is NA to 12(9+3)

Constraint
R.H. Side	Range
7200	7440	4400
6600	NA	6300
600	1000	514.2857
200	900	100
1000	NA	600
1000	NA	700

Range = Constraint RHS + Allowable increase to  Constraint RHS - Allowable decrease

D) If more time is available on grinder it will be worth 0 since shadow price is 0

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Bouk1 Microsoft Excel Home InsertPage Layout Formulas D Review View ovaPOF Clear Show Detl Dats Analyss ฐ Properties From From From From Other Existing Retresh Access Web Tet SourcesConnectionslFdit Links to Remove Dats Consolidate What-r Group Ungroup Subtotal Advanced Columns Duplicates Validation Get Estermnal Data Dats Tools A6 Adjustable Cells 1 Microsoft Excel 12.0 Sensitivity Report 3 Report Created: 4/29/2017 11:10:01 AM 6 Adjustable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coelficient Increase Decrease 9 SE514 Var Ci 600 1E+30 11 SG$14 Var C3 200 12 13 Constraints Final Shadow Constraint Allowable Allowable 15 Cell Name Value Price R.H. side Increase Decrease 16 $G$19 C3 7200 6300 E 30 18 56524 C3 19 $527 C3 20 SG$30 C3 21 SG$32 C3 400 85.71428571 100 1000 1E+30 1000 E+20 25 26 27 30 31 1Answer Sheet1Sheet2 Sh 11:13 AM Type here to search ENGA292017