1.The Employee Credit Union at Directional State University is planning the allocation of funds for the coming year.ECU makes four types of loans and has three additional investment instruments.Each loan/investment has a corresponding risk and liquidity factor (on a scale of 0-100, with 100 being the most risky/liquid).The various revenue-producing instruments are summarized in the table below:
Instrument |
Annual Rate of Return (%) |
Risk Factor |
Liquidity Factor |
Automobile loans |
8 |
50 |
0 |
Furniture loans |
10 |
60 |
0 |
Other secured loans |
11 |
70 |
0 |
Unsecured loans |
14 |
80 |
0 |
Risk-free securities |
5 |
0 |
100 |
Corporate stock fund |
9 |
60 |
90 |
Corporate bond fund |
8 |
50 |
80 |
ECU has $2,000,000 available for investment during the coming year.However, state laws and pesky stakeholders impose certain restrictions on choice of investment instruments.Risk-free securities may not exceed 40% of total funds available for investment.Unsecured loans may not exceed 10% of total funds invested in loans.The funds invested in automobile loans must not be less than the total of funds invested in furniture and other secured loans.The average risk factor may not exceed 60, and the average liquidity factor must be at least 40.Formulate a linear program for ECU.(14)
Check each of the following that apply.
There are seven decision variables.____
There are six constraints (not counting nonnegativity).____
We determine the average risk factor by summing risk values and dividing by 7.____
Risk-free security total investment may exceed $800,000.____
All $2,000,000 must be invested.____
This is a maximization problem.____
This problem cannot be run as an integer program.____
Check all that apply.
This is a basic EOQ problem.____
The optimal order quantity is greater than 500 units.____
If their current order policy is to order 600 units, the total annual cost would increase.____
If the holding cost were to increase to 25%, the optimal order quantity would increase.____
If they started to produce this component, total cost would decline.____
If annual demand changed to 20,000 units, the optimal order quantity would double.____
If the order cost increased, the optimal number of orders/year would decrease.____
In this model, the service level is 100%.____
Check all that apply.
The optimal order quantity (EOQ) for $38 would be the optimal order quantity for the overall problem.____
The optimal order quantity would be the same as in #2.____
The optimal order quantity would be larger than in #2.
The procurement cost is not relevant since it is incurred regardless of order quantity.____
_________
________
Yes_____
No______
None____
Increase the optimal profit______
Decrease the final profit______
LINEAR PROGRAMMING PROBLEM
MAX 6X1+7X2+4X3+7X4-200X5
S.T.
1)1X1+1X2+1X3<1000
2)1X3-1X4>20
3)4X1+4X2+3X3+3X4<12000
4)3X1+6X2+4X3+5X4<14000
5)1X2+1X4-600X5>0
6)1X2+1X4-380X5<600
OPTIMAL SOLUTION
Objective Function Value =10660.000
VariableValueReduced Costs
———————————————–
X10.0004.474
X20.0004.000
X31000.000 0.000
X4980.0000.000
X51.0000.000
ConstraintSlack/SurplusDual Prices
———————————————–
10.00010.474
20.000-6.474
36060.0000.000
45100.0000.000
5380.0000.000
60.0000.526
OBJECTIVE COEFFICIENT RANGES
VariableLower LimitCurrent ValueUpper Limit
———————————————————
X1No Lower Limit6.00010.474
X2No Lower Limit7.00011.000
X30.0004.000No Upper Limit
X43.0007.000No Upper Limit
X5-1900.000-200.0000.000
RIGHT HAND SIDE RANGES
ConstraintLower LimitCurrent ValueUpper Limit
———————————————————
1620.0001000.0001566.667
2-636.36420.000400.000
35940.00012000.000No Upper Limit
48900.00014000.000No Upper Limit
5No Lower Limit0.000380.000
6359.333600.000980.000