QM 670 Exam II Name____________________ This exam is worth 50 points. (Four are free.) Please read the instructions carefully on each problem. 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.____ 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%.____ 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.____ 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). Which constraints are binding? (2) _________ Which constraint would we prefer to see relaxed? (2) ________ 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______ 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 RIGHT HAND SIDE RANGES Constraint Lower Limit Current Value Upper Limit ———— ————— ————— ————— 1 620.000 1000.000 1566.667 2 -636.364 20.000 400.000 3 5940.000 12000.000 No Upper Limit 4 8900.000 14000.000 No Upper Limit 5 No Lower Limit 0.000 380.000 6 359.333 600.000 980.000