.The Employee Credit Union at Directional State University, assignment help

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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.____


______________________________________________________________________________________________

2. A local company orders a component part at $40/unit. The cost of placing an order is $100, and the annual cost of holding a unit in inventory is 20%. Current annual demand is 10,000 units, demand is treated as known and at a constant rate, and backorders are not allowed. (16)

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%.____

_________________________________________________________________________________

Question 3:

In #2, suppose you receive a quantity discount such that for orders of at least 600 the cost per unit of the component is $38? (8)

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.____

____________________________________________________________________________________


  1. See the following Management Scientist output. In this problem, we are trying to determine the optimal number of rolls of four types of fabric (1, 2, 3, and 4) to produce. Note that the third constraint concerns the available quantity of a certain chemical resin used for each type of fabric, the fourth constraint concerns the available quantity of polyester, and the final two constraints are imposed to ensure that we will incur a $200 penalty if we produce at least 600 units of Types 2 and 4 (since this will require us to redeploy an additional production line). A) Which constraints are binding? (2) _________________ B) Which constraint would we prefer to see relaxed? (2) _____________
  2. C) Nora in Accounting realized that the profit associated with Type 1 fabric should be $8.00/unit. Will this have an effect on the optimal solution? (2) Yes _________________ No ______________
  1. If the availability of the chemical (third constraint) were 15,000, what effect would this have? (2)

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

Variable Value Reduced Costs

-------------- --------------- ------------------

X1 0.000 4.474

X2 0.000 4.000

X3 1000.000 0.000

X4 980.000 0.000

X5 1.000 0.000

Constraint Slack/Surplus Dual Prices

-------------- --------------- ------------------

1 0.000 10.474

2 0.000 -6.474

3 6060.000 0.000

4 5100.000 0.000

5 380.000 0.000

6 0.000 0.526


OBJECTIVE COEFFICIENT RANGES

Variable Lower Limit Current Value Upper Limit

------------ --------------- --------------- ---------------

X1 No Lower Limit 6.000 10.474

X2 No Lower Limit 7.000 11.000

X3 0.000 4.000 No Upper Limit

X4 3.000 7.000 No Upper Limit

X5 -1900.000 -200.000 0.000

Unformatted Attachment Preview

Name____________________ 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 Automobile loans Furniture loans Other secured loans Unsecured loans Risk-free securities Corporate stock fund Corporate bond fund Annual Rate of Return (%) 8 10 11 14 5 9 8 Risk Factor 50 60 70 80 0 60 50 Liquidity Factor 0 0 0 0 100 90 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.____ 2. A local company orders a component part at $40/unit. The cost of placing an order is $100, and the annual cost of holding a unit in inventory is 20%. Current annual demand is 10,000 units, demand is treated as known and at a constant rate, and backorders are not allowed. (16) 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%.____ 3. In #2, suppose you receive a quantity discount such that for orders of at least 600 the cost per unit of the component is $38? (8) 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.____ 4. See the following Management Scientist output. In this problem, we are trying to determine the optimal number of rolls of four types of fabric (1, 2, 3, and 4) to produce. Note that the third constraint concerns the available quantity of a certain chemical resin used for each type of fabric, the fourth constraint concerns the available quantity of polyester, and the final two constraints are imposed to ensure that we will incur a $200 penalty if we produce at least 600 units of Types 2 and 4 (since this will require us to redeploy an additional production line). A. Which constraints are binding? (2) _________ B. Which constraint would we prefer to see relaxed? (2) ________ C. Nora in Accounting realized that the profit associated with Type 1 fabric should be $8.00/unit. Will this have an effect on the optimal solution? (2) Yes_____ No______ D. If the availability of the chemical (third constraint) were 15,000, what effect would this have? (2) None____ Increase the optimal profit______ Decrease the final profit______ LINEAR PROGRAMMING PROBLEM MAX 6X1+7X2+4X3+7X4-200X5 S.T. 1) 2) 3) 4) 5) 6) 1X1+1X2+1X320 4X1+4X2+3X3+3X4
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Explanation & Answer

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Question 1
The following conditions apply:
• There are seven decision variables which include: automobiles loans, furniture loans,
other secured loans, unsecured loans, risk-free securities, corporate stock fund, and
corporate bond fund.


There are 6 constraints - there are six linear inequalities excluding nonnegative
inequality.





All $2000000 must be invested condition applies.
Risk-free security total investment may exceed $800,000
This is a maximization problem- the problem aims at optimizing income.

Question 2
It is an EOQ problem due to the following reasons:


There is only one product (component part) involved.



Annual demand is known that is 10000 units.



Demand is constant.



Lead time does not vary.



Back orders are not allowed.

Optimal order quantity
At 20% annual cost holding unit in an inventory the EOQ will be;
2∗𝑞𝑢𝑎𝑛𝑡𝑖𝑡𝑦∗𝑐𝑜𝑠𝑡 𝑝𝑒𝑟 𝑜𝑟𝑑𝑒𝑟
𝑐𝑎𝑟𝑟𝑦𝑖𝑛𝑔 𝑐𝑜𝑠𝑡 𝑝𝑒𝑟 𝑜𝑟𝑑𝑒𝑟

EOQ = √

2∗10000∗100
20%∗10000

=√

= 31.622
Comment: The optimal order quantity is less than 500.
At 25% annual cost holding unit in an inventory the EOQ will be
2∗𝑞𝑢𝑎𝑛𝑡𝑖𝑡𝑦∗𝑐𝑜𝑠𝑡 𝑝𝑒𝑟 𝑜𝑟𝑑𝑒𝑟
𝑐𝑎𝑟𝑟𝑦𝑖𝑛𝑔 𝑐𝑜𝑠𝑡 𝑝𝑒𝑟 𝑜𝑟𝑑𝑒𝑟

EOQ = √

2∗10000∗100

=√ 25%∗10000

=28.28
Comment: increase in annual cost holding unit in an inventory will decrease the optimal order quantity.

If annual demand changed to 20,000 units, the optimal order quantity would double?
2∗𝑞𝑢𝑎𝑛𝑡𝑖𝑡𝑦∗...


Anonymous
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