1_ (10pts)
The decision variables of the given LP model determines how many necklaces (X1), bracelets(X2), rings (X3), and earrings (X4) a jewelry store should stock. The objective function measures profit.
Constraint-1 measures display space in units, constraint-2 measures time to set up the display in minutes. Constraints-3 and constraint-4 are marketing restrictions.
MAX = $100X1+$120X2+$150X3+$125X4
Constraints
c1) X1+2X2+2X3+2X4 ≤ 108
c2) 3X1+5X2+X4 ≤ 120
c3) X1+X3 ≤ 25
c4) X2+X3+X4 ≥ 50
a) Provide the sensitivity analysis report
b) How many necklaces, bracelets, rings, and earrings should be stocked? What is the total profit?
c) How much space will be left unused?
d) How much time will be used?
e) By how much will the second marketing restriction be exceeded?
f) Find the total profit after increasing the unit profit of rings and earrings by $5 simultaneously.
g) Find the new total profit after decreasing the time to set up the display by 65 minutes.
h) You are offered the chance to obtain more space. The offer is for 15 units and the cost of increasing the space is $1500. Would you accept this offer? Why?
2_(10pts)
The distribution system for the Smith Company consists of three plants (A, B, C, and D), three warehouses (E, F, and G), and four customers (W, X, Y, and Z). The relevant supply, demand, and unit shipping cost information are given in the tables below. Set up and solve the transshipment model to minimize total shipping costs.
|
Plant |
Supply |
|
Customer |
Demand |
|
A |
450 |
|
W |
450 |
|
B |
490 |
|
X |
300 |
|
C |
310 |
|
Y |
300 |
|
D |
150 |
|
Z |
400 |
|
From/To |
E |
F |
G |
|
From / To |
W |
X |
Y |
Z |
|
A |
$4 |
$7 |
$6 |
|
E |
$6 |
$4 |
$8 |
$4 |
|
B |
$8 |
$5 |
$9 |
|
F |
$3 |
$6 |
$7 |
$7 |
|
C |
$5 |
$6 |
$11 |
|
G |
$5 |
$9 |
$13 |
$8 |
|
D |
$6 |
$4 |
$10 |
|
|
|
|
|
|
(Provide LP model and the Excel solver Results in the given Excel Answer File)
3_(10pts)
Porter Investments needs to develop an investment portfolio for Mrs. Singh from the following list of possible investments:
| Investment |
Cost |
Expected Return |
| A |
$ 15,000 |
$800 |
| B |
$ 13,000 |
$1,300 |
| C |
$ 8,500 |
$550 |
| D |
$ 6,500 |
$900 |
| E |
$ 10,000 |
$360 |
| F |
$ 7,000 |
$760 |
| G |
$ 10,500 |
$400 |
Mrs. Singh has a total of $75,000 to invest. The following conditions must be met: (1) If investment A is chosen, then investment C must also be part of the portfolio, (2) No more than 5 investments should be chosen, (3) of investment B and G, exactly one must be included, and (4) at least 3 investment should be chosen. What stocks should be included in Mrs. Singh’s portfolio?
(Provide LP model and the Excel solver Results in the given Excel Answer File)
4_(10pts)
A snowmobile manufacturer produces three models, the SM1, the SM2, and the SM3. In any given production-planning week, the company has 60 hours available in its final testing bay. Each SM1 requires 2 hour of testing, each SM2 requires 3 hours, and each SM3 takes 4.5 hours. The revenue (in $thousands) per unit of each model is defined as ($3+ $2.5X1) for SM1, ($5 – $0.3X2) for SM2, and ($4 + $0.7X3) for SM3, where X1 , X2 , and X3 are the numbers of SM1, SM2, and SM3 models made, respectively. In addition, the required raw material is 10 units, 15 units and 8 units for each snowmobile respectively while there is 1500 tons of available raw material. Each unit of raw material was defined as “0.04*X1 ton”. Formulate this problem to maximize revenue and solve it by using Excel. Use several different starting values for the decision variables to try to identify a global optimal solution.
|
|
SM1 |
SM2 |
SM3 |
Available (Up to) |
|
Testing hours |
2 Hours |
3 Hours |
4.5 Hours |
60 Hours |
|
Raw Material |
10 units |
15 units |
8 units |
1500 Ton |
|
Unit Profit |
($3+$2.5X1) |
($5 – $0.3X2) |
($4 + $0.7X3) |
|
|
1 Unit of Raw Material = (0.04X1) Ton |
||||
(Provide LP model and the Excel solver Results in the given Excel Answer File)
5_(10pts)
A hospital is planning an $8 million addition to its existing facility. The architect has been asked to consider the following design parameters:
There should be at least 10 and no more than 20 intensive care unit (ICU) rooms;
there should be at least 10 and no more than 20 cardiac care unit (CCU) rooms;
there should be no more than 50 double rooms;
there should be at least 35 single rooms; and
all patient rooms should fit inside the allotted 40,000-square-foot space (not including hallways).
The following table summarizes the relevant room data:
|
Single |
Double |
ICU |
CCU |
|
|
Cost per room to build and furnish ($thousands) |
$45 |
$54 |
$110 |
$104 |
|
Minimum square feet required |
300 |
360 |
320 |
340 |
|
Profit per room per month ($thousands) |
$21 |
$28 |
$ 48 |
$ 41 |
Find the numbers of rooms of each type should the architect include in the new hospital design using an appropriate decision making model.
Hint: Ensure that the number of rooms is not fractional.
(Provide the LP model and the Excel solver Results in the given Excel Answer File)
6_ (10pts)
The values on the arcs represent the distance, in miles. Find the shortest route between the 1st and the 6th city using network model approach.
(Excel solver Result is sufficient, you do not have to provide LP model)
