Round Tree Manor is a hotel that provides two types of rooms with three rental classes: Super Saver, Deluxe, and Business. The profit per night for each type of room and rental class is as follows:
Rental Class
Room Super Saver Deluxe Business
Type I $30 $35 -
Type II $20 $30 $40
Type I rooms do not have Internet access and are not available for the Business rental class.
Round Tree's management makes a forecast of the demand by rental class for each night in the future. A linear programming model developed to maximize profit is used to determine how many reservations to accept for each rental class. The demand forecast for a particular night is 130 rentals in the Super Saver class, 60 rentals in the Deluxe class, and 50 rentals in the Business class. Round Tree has 100 Type I rooms and 120 Type II rooms.
Question 1: How many reservations can be accomodated in each rental class? Choose one answer.
A. 100-Super Saver; 30-Deluxe; 90-Business
B. 126-Super Saver; 60-Deluxe; 48-Business
C. 120-Super Saver; 60-Deluxe; 50-Business
D. 110-Super Saver; 60-Deluxe; 50-Business
Question 2: Please refer to Question 1.
What is the value of the objective function? Choose one answer.
A. $6,800
B. $7,150
C. $7,000
D. $6,420
Question 3: Are the demands of all rental classes satisfied? Explain. Choose one answer.
A. Only Deluxe rental class demand is satisfied.
B. Only Business rental class demand is satisfied.
C. Only Super Saver and Deluxe rental classes' demands are satisfied
D. Only Deluxe and Business rental classes' demands are satisfied.
Question 4: Management is considering offering a free breakfast to anyone upgrading from a Super Saver reservation to Deluxe class. If the cost of the breakfast to Round Tree is $10, should this incentive be offered? Choose one answer.
A. The incentive should be offered only for the deluxe rental class.
B. Yes; the overall profit is improved.
C. The incentive should be offered only for the business rental class.
D. No; the overall additional cost decreases the profit.
The employee credit union at State University is planning the allocation of funds for the coming year. The credit union makes four types of loans to its members. In addition, the credit union invests in risk-free securities to stabilize income. The various revenue-producing investments together with annual rates of return (ARR) are as follows:
Type of Loan/Investment ARR (%)
Automobile loans, X1 8
Furniture loans, X2 10
Other secured loans, X3 11
Signature loans, X4 12
Risk-free securities, X5 9
The credit union will have a $2 million available for investment during the coming year. State laws and credit union policies impose the following restrictions on the composition of the loans and investments.
- Risk-free securities may not exceed 30% of the total funds available for investment.
- Signature loans may not exceed 10% of the funds invested in all loans (automobile, furniture, other secured, and signature loans).
- Furniture loans plus other secured loans may not exceed the automobile loans.
- Other secured loans plus signature loans may not exceed the funds invested in risk-free securities.
Question 5: How should the $2,000,000 be allocated to each of the loan/investment alternatives to maximize total annual return? Choose one answer.
A. X1=$600K; X2=$300K; X3=$310K; X4=$200K; X5=$590K
B. X1=$650K; X2=$200K; X3=$300K; X4=$250K; X5=$600K
C. X1=$600K; X2=$190K; X3=$460K; X4=$150K; X5=$600K
D. X1=$630K; X2=$170K; X3=$460K; X4=$140K; X5=$600K
Question 6: What is the projected annual return?
A. 18.88 %
B. 9.44 %
C. 11.61 %
D. 10.77 %
Question 7: Golf Shafts, Inc. (GSI), produces graphite shafts for several manufacturers of golf clubs. Three GSI manufacturing facilities, one located in San Diego, one in Tampa, and the other in Boston have the capability to produce shafts in varying degrees of stiffness, ranging from regular models used primarily by average golfers to extra stiff models used primarily by low-handicap and professional golfers. GSI just received a contract for the production of 200,000 regular shafts and 175,000 stiff shafts. Because all plants are currently producing shafts for previous orders, neither plant has sufficient capacity by itself to fill the new order. The San Diego plant can produce up to a total of 170,000 shafts, the Tampa plant can produce up to a total of 100,000 shafts, and the Boston plant can produce up to a total of 105,000 shafts. Because of equipment differences at each of the plants and differing labor costs, the per-unit production costs vary as shown here:
San Diego Cost Tampa Cost Boston Cost
Regular shaft $5.25 $4.95 $5.05
Stiff shaft $5.45 $5.70 $5.32
a. How many regular shafts are to be produced in San Diego, Tampa and Boston plants respectively in order to minimize the cost? Choose one answer.
A. 14250; 118450; 67300
B. 26512; 102246; 71242
C. 0; 100000; 100000
D. 10000; 105000; 85000
Question 8: How many shafts (regular+stiff) in total do San Diego, Tampa and Boston plants have to produce in order to minimize the cost? Choose one answer.
A. 175000; 95000; 105000
B. 182000; 100000; 93000
C. 170000; 100000; 105000
D. 165000; 100000; 110000
Question 9: What is the value of the objective function? Choose one answer.
A. $1,998,503
B. $1,953,100
C. $2,001,600
D. $1,857,400
Question 10: Suppose that some of the previous orders at the Tampa plant could be rescheduled in order to free up additional capacity for the new order. Would this option be worthwhile? Why? Choose one answer.
A. No; the surplus would increase the cost.
B. Yes; the cost of production would further be minimized.
C. No; there would be no change in the value of the objective function.
D. Yes; let's give it a try!
Question 11: Suppose that the cost to produce a stiff shaft in Tampa had been incorrectly computed, and that the correct cost is $5.30 per shaft. What effect, if any, would the correct cost have on the original optimal solution? What effect would it have on total production cost (TPC)? Choose one answer.
A. The objective function changes and TPC decreases.
B. No effect on the objective solution; however TPC would decrease.
C. No change in the objective function and TPC remains the same.
D. No effect at all; TPC would remain the same.
Question 12: Edwards Manufacturing Company purchases two component parts from three different suppliers. The suppliers have limited capacity, and no one supplier can meet all the company's needs. In addition, the suppliers charge different prices for the components. Component price data (in price per unit) are as follows:
Supplier
Component 1 2 3
1 $12 $13 $14
2 $10 $11 $10
Each supplier has a limited capacity in terms of the total number of components it can supply. However, as long as Edwards provides sufficient advance orders, each supplier can devote its capacity to component 1, component 2, or any combination of the two components, if the total number of units ordered is within its capacity. Supplier capacities are as follows.
Supplier 1 2 3
Capacity 600 1000 800
If the Edwards production plan for the next period includes 1000 units of component 1 and 800 units of component 2, how many units of each component (C1, C2) should be ordered from each supplier (S1, S2, S3)?
Choose one answer.
A. C1; S1=400, S2=400, S3=200 / C2; S1=200, S3=600
B. C1; S1=800, S2=200 / C2; S1=200, S3=600
C. C1; S1=600, S2=400 / C2; S3=800
D. C1; S1=1000 / C2; S3=800
Question 13: What is the total purchase cost for the components? Choose one answer.
A. $19,800
B. $20, 624
C. $20,200
D. $20,400
Question 14: Hart Manufacturing makes three products. Each product requires manufacturing operations in three departments: A, B, and C. The labor-hour requirements, by department, are as follows:
Department Product 1 Product 2 Product 3
A 1.50 3.00 2.00
B 2.00 1.00 2.50
C 0.25 0.25 0.25
During the next production period, the labor-hours available are 450 in department A, 350 in department B, and 50 in department C. The profit contributions per unit are $25 for product 1, $28 for product 2, and $30 for product 3.
How many units of product does each department have to manufacture to maximize the profit? Choose one answer.
A. A=100; B=250; C=450
B. A=175; B=225; C=346
C. A=300; B=350; C=200
D. A=250; B=250; C=300
Question 15: What is the maximum profit Hart Company can make with the current resources?
A. $22,250
B. $21,055
C. $23,000
D. $23,300
Question 16; One of the production supervisors noted that production setup costs had not been taken into account. She noted that setup costs are $400 for product 1, $550 for product 2, and $600 for product 3. If the previous solution is to be used, what is the total profit contribution after taking into account the setup costs? Choose one answer.
A. $20,700
B. $21,450
C. $21,750
D. $19,800
Question 17: Management realized that the optimal product mix, taking setup costs into account, might be different from the previous solution. Formulate a mixed-integer linear program that takes setup costs into account. Management also stated that we should not consider making more than 175 units of product 1, 150 units of product 2, or 140 units of product 3. How many units of product should each department produce? Choose one answer.
A. A=213; B=208; C=127
B. A=197; B=175; C=93
C. A=180; B=185; C=90
D. A=220; B=175; C=70
Question 18: What is the projected total profit with the setup costs and new constraints taken into account? Choose one answer.
A. $21,200
B. $12,600
C. $9,180
D. $11,225
Question 19: Hamilton County Parks is planning to develop a new park and recreational area on a recently purchased 100-acre tract. Project development activites include clearing playground and picnic areas, constructing roads, constructing a shelter house, purchasing picnic equipment, and so on. The following network and activity times (in weeks) are being used in the planning, scheduling, and controlling of this project. What is the critical path for this network Choose one answer.
A. B-F-G-I
B. B-E-H-I
C. A-C-E-H-I
D. A-D-H-I
Question 20: What is the activity completion time of the project? Choose one answer.
A. 21 weeks
B. 15 weeks
C. 24 weeks
D. 26 weeks