Showing Page:
1/4
a. What are the optimal solution
DRB
DRW
variable
1000
800
PROFIT
200
280
Available
constraint 1
20
25
<=
40000
40000
constraint 2
40
100
<=
120000
120000
constraint 3
20
40
<=
52000
96000
Total Profit
424000
The optimal solution:
DRB is 1000
DRW is 800
The total profit is \$424,000
b.
The shadow price for assembly time constraint indicates that the value of the optimal
solution will improve at a rate of \$0.6 per hour
c.
The shadow price for the manufacturing time constraint will simply add to the mount of
slack for constraint and will not change the value of optimal solution.
d.
DRB
DRW
variable
1000
800
PROFIT
175
280
Available
constraint 1
20
25
<=
40000
40000
constraint 2
40
100
<=
120000
120000
Showing Page:
2/4
constraint 3
20
40
<=
52000
96000
Total Profit
399000
Thus with the revised objective function coefficient and the same optimal solution, the
total profit contribution becomes \$399000.
e. The shadow price for assembly time constraint indicates that the value of the optimal
solution will improve at the rate of \$8.8 per pound.
Question 27
a.
Total demand = 200,000 regular shafts +75000 stiff shafts = 275000
Let San Diego produce “a” regular shafts, “b” stiff shafts. Let Tampa produce “c” regular
shaft, “d” stiff shafts.
Cost = 5.25a + 5.45b+4.95c+5.70d
This is our objective function and has to be minimized. Constraints are:
i. a+b+c+d = 275000 (production = demand)
ii. a+c = 200000(demand for regular shafts = production for regular shafts)
iii. b+d = 75000 (production of stiff shafts = demand for stiff shafts)
iv. a+b <= 120000 (capacity of San Diego )
v. c+d <= 180000 (capacity of Tampa)
vi. a, b, c, d >= 0
b.
b
c
d
Variable
0
80000
75000
Cost
5.45
4.95
5.7
Showing Page:
3/4
required
Available
constraint 1
1
1
1
<=
275000
275000
constraint 2
0
1
0
<=
200000
200000
constraint 3
1
0
1
<=
75000
75000
constraint 4
1
0
0
<=
120000
120000
constraint 5
0
1
1
<=
155000
180000
constraint 6
1
1
1
>=
275000
0
Total cost
Thus San Diego will produce 120,000 regular shafts. Tampa will make 80000 regular and
75000 stiff shafts. Total minimized costs = \$ 1453500.
c.
If the capacity of Tampa is freed up, then the capacity constraint for Tampa will be
removed from the model that is (c+d <= 180000).
b
c
d
Variable
0
80000
75000
Cost
5.45
4.95
5.7
required
Available
constraint 1
1
1
1
<=
275000
275000
constraint 2
0
1
0
<=
200000
200000
constraint 3
1
0
1
<=
75000
75000
constraint 4
1
0
0
<=
120000
120000
constraint 5
1
1
1
>=
275000
0
Total cost
The costs remains the same thus San Diego will produce 120,000 regular shafts. Tampa
will make 80000 regular and 75000 stiff shafts. Total minimized costs = \$ 1453500.
d.
a
b
c
d
Variable
120000
0
80000
75000
Cost
5.25
5.45
4.95
5.3
Required
Available
Showing Page:
4/4
constraint 1
1
1
1
1
<=
275000
275000
constraint 2
1
0
1
0
<=
200000
200000
constraint 3
0
1
0
1
<=
75000
75000
constraint 4
1
1
0
0
<=
120000
120000
constraint 5
0
0
1
1
<=
155000
180000
constraint 6
1
1
1
1
>=
275000
0
Total cost
1423500
If the cost of making stiff shaft by Tampa is lowered to \$5.30 then the total costs will be
minimized to \$1423500. Thus San Diego will produce 120,000 regular shafts. Tampa
will make 80000 regular and 75000 stiff shafts.

### Unformatted Attachment Preview

a. What are the optimal solution DRB DRW 1000 800 200 280 variable PROFIT constraint 1 constraint 2 constraint 3 20 40 20 Total Profit 424000 25 <= 100 <= 40 <= Available 40000 40000 120000 120000 52000 96000 The optimal solution: DRB is 1000 DRW is 800 The total profit is \$424,000 b. The shadow price for assembly time constraint indicates that the value of the optimal solution will improve at a rate of \$0.6 per hour c. The shadow price for the manufacturing time constraint will simply add to the mount of slack for constraint and will not change the value of optimal solution. d. variable PROFIT constraint 1 constraint 2 DRB DRW 1000 800 175 280 20 40 25 <= 100 <= Available 40000 40000 120000 120000 constraint 3 20 Total Profit 399000 40 <= 52000 96000 Thus with the revised objective function coefficient and the same optimal solution, the total profit contribution becomes \$399000. e. The shadow price for assembly time constraint indicates that the value of the optimal solution will improve at the rate of \$8.8 per pound. Question 27 a. Total demand = 200,000 regular shafts +75000 stiff shafts = 275000 Let San Diego produce “a” regular shafts, “b” stiff shafts. Let Tampa produce “c” regular shaft, “d” stiff shafts. Cost = 5.25a + 5.45b+4.95c+5.70d This is our objective function and has to be minimized. Constraints are: i. a+b+c+d = 275000 (production = demand) ii. a+c = 200000(demand for regular shafts = production for regular shafts) iii. b+d = 75000 (production of stiff shafts = demand for stiff shafts) iv. a+b <= 120000 (capacity of San Diego ) v. c+d <= 180000 (capacity of Tampa) vi. a, b, c, d >= 0 b. a Variable Cost b 120000 5.25 c 0 5.45 d 80000 4.95 75000 5.7 constraint 1 constraint 2 constraint 3 constraint 4 constraint 5 constraint 6 Total cost 1 1 0 1 0 1 1453500 1 0 1 1 0 1 1 1 0 0 1 1 1 0 1 0 1 1 <= <= <= <= <= >= required Available 275000 275000 200000 200000 75000 75000 120000 120000 155000 180000 275000 0 Thus San Diego will produce 120,000 regular shafts. Tampa will make 80000 regular and 75000 stiff shafts. Total minimized costs = \$ 1453500. c. If the capacity of Tampa is freed up, then the capacity constraint for Tampa will be removed from the model that is (c+d <= 180000). a Variable Cost b 120000 5.25 constraint 1 constraint 2 constraint 3 constraint 4 constraint 5 Total cost 1 1 0 1 1 c 0 5.45 d 80000 4.95 1 0 1 1 1 75000 5.7 1 1 0 0 1 1 0 1 0 1 <= <= <= <= >= required Available 275000 275000 200000 200000 75000 75000 120000 120000 275000 0 1453500 The costs remains the same thus San Diego will produce 120,000 regular shafts. Tampa will make 80000 regular and 75000 stiff shafts. Total minimized costs = \$ 1453500. d. a Variable Cost b 120000 5.25 c 0 5.45 d 80000 4.95 75000 5.3 Required Available constraint 1 constraint 2 constraint 3 constraint 4 constraint 5 constraint 6 Total cost 1 1 0 1 0 1 1423500 1 0 1 1 0 1 1 1 0 0 1 1 1 0 1 0 1 1 <= <= <= <= <= >= 275000 200000 75000 120000 155000 275000 275000 200000 75000 120000 180000 0 If the cost of making stiff shaft by Tampa is lowered to \$5.30 then the total costs will be minimized to \$1423500. Thus San Diego will produce 120,000 regular shafts. Tampa will make 80000 regular and 75000 stiff shafts. Name: Description: ...
User generated content is uploaded by users for the purposes of learning and should be used following Studypool's honor code & terms of service.
Studypool
4.7
Trustpilot
4.5
Sitejabber
4.4