8-5 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 Delux e Business Type I $35 $40 - Type II $15 $25 $35 Type I rooms do not have wireless 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 140 rentals in the Super Saver class, 65 rentals in the Deluxe class, and 40 rentals in the Business class. Round Tree has 100 Type I rooms and 120 Type II rooms. (a) Use linear programming to determine how many reservations to accept in each rental class and how the reservations should be allocated to room types. Rental Class with room type No of Reservations Super Saver rentals allocated to room type I Super Saver rentals allocated to room type II Deluxe rentals allocated to room type I Deluxe rentals allocated to room type II Business rentals allocated to room type II Demand by - Select your answer -DeluxeSuper SaverBusinessItem 6 rental class was not satisfied. Explain. The input in the box below will not be graded, but may be reviewed and considered by your instructor. (b) How many reservations can be accommodated in each rental class? Rental Class No of Reservations Super Saver I ___________________ Deluxe ___________________ Business _____________________ (c) 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 $5, should this incentive be offered? - Select your answer -Yes or no Explain. The input in the box below will not be graded, but may be reviewed and considered by your instructor. (d) With a little work, an unused office area could be converted to a rental room. If the conversion cost is the same for both types of rooms, would you recommend converting the office to a Type I or a Type II room? Shadow Price Type I Type II $ $ Convert an unused office area to - Select your answer -Type IType IIItem 15 room. Explain. The input in the box below will not be graded, but may be reviewed and considered by your instructor. (e) Could the linear programming model be modified to plan for the allocation of rental demand for the next night? - Select your answer -(yes or no) 17 What information would be needed and how would the model change? Explain. The input in the box below will not be graded, but may be reviewed and considered by your instructor. Problem 8-7 Vollmer Manufacturing makes three components for sale to refrigeration companies. The components are processed on two machines: a shaper and a grinder. The times (in minutes) required on each machine are as follows: Machine Component Shape r Grinder 1 6 4 2 4 5 3 4 2 The shaper is available for 120 hours, and the grinder is available for 110 hours. No more than 200 units of component 3 can be sold, but up to 1000 units of each of the other components can be sold. In fact, the company already has orders for 600 units of component 1 that must be satisfied. The profit contributions for components 1, 2, and 3 are $8, $6, and $9, respectively. (a) Formulate and solve for the recommended production quantities. Let C1 = units of component 1 manufactured C2 = units of component 2 manufactured C3 = units of component 3 manufactured Max C1 + C2 + C3 C1 + ____C2 + ______C3 - Select your answer -=Item 7 Shaper C1 + _____C2 + ______C3 - Select your Grinder s.t. ____ ____ answer -=Item 12 _________ C3 _______ C1 ___________ C2 ______C1 C1, C2, C3 - Select your answer -=Item 15 Maximum units of component 3 - Select your answer -=Item 18 Maximum units of component 1 - Select your answer -=Item 21 Maximum units of component 2 - Select your answer -=Item 24 Minimum units of component 1 - Select your answer -=Item 26 0 Optimal solution: C1, = ______ , C2, = ________ , C3= ___________ (b) What are the objective coefficients ranges for the three components? Variable Objective Coefficient Range C1 - Select your answer -No Lower Limit7.335.466.00Item 30 to - Select your answer -No Upper Limit9.008.569.50Item 31 C2 - Select your answer -No Lower Limit4.335.336.00Item 32 to - Select your answer -No Upper Limit9.008.5610.00Item 33 C3 - Select your answer -No Lower Limit5.005.506.00Item 34 to - Select your answer -No Upper Limit10.009.509.00Item 35 Interpret these ranges for company management. The input in the box below will not be graded, but may be reviewed and considered by your instructor. (c) What are the right-hand-side ranges? Constraint Right-Hand-Side Range 1 - Select your answer -No Lower Limit430044004500Item 37 to - Select your answer -No Upper Limit744075007550Item 38 2 - Select your answer -No Lower Limit433053306300Item 39 to - Select your answer -No Upper Limit850072006600Item 40 Interpret these ranges for company management. The input in the box below will not be graded, but may be reviewed and considered by your instructor. (d) If more time could be made available on the grinder, how much would it be worth? - Select your answer -Profit of $1000Profit of $200NothingItem 42 Explain. The input in the box below will not be graded, but may be reviewed and considered by your instructor. (e) If more units of component 3 can be sold by reducing the sales price by $4, should the company reduce the price? - Select your answer -Yes or no) Explain. The input in the box below will not be graded, but may be reviewed and considered by your instructor. Problem 8-9 The Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this year's program. Advertising alternatives include television, radio, and newspaper. Audience estimates, costs, and maximum media usage limitations are as shown: Constraint Television Radio 110,000 18,000 30,000 Cost per advertisement $1,500 $250 $500 Maximum media usage 11 21 13 Audience per advertisement Newspaper To ensure a balanced use of advertising media, radio advertisements must not exceed 50% of the total number of advertisements authorized. In addition, television should account for at least 10% of the total number of advertisements authorized. (a) If the promotional budget is limited to $23,000, how many commercial messages should be run on each medium to maximize total audience contact? Advertisement Alternatives No of commercial messages Television ______________ Radio ______________ Newspaper _______________ What is the allocation of the budget among the three media? Advertisement Alternatives Budget ($) Television $ _____ Radio $ ______ Newspaper $ ________ What is the total audience reached? ________________ (b) By how much would audience contact increase if an extra $100 were allocated to the promotional budget? Increase in audience coverage of approximately _______________ Problem 8-11 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 are as follows: Type of Loan/Investment Annual Rate of Return (%) Automobile loans 8 Furniture loans 10 Other secured loans 11 Signature loans 12 Risk-free securities 9 The credit union will have $1.8 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 25% of the total funds available for investment. Signature loans may not exceed 12% 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. How should the $1.8 million be allocated to each of the loan/investment alternatives to maximize total annual return? Type of Loan/Investment Fund Allocation Automobile loans $__________ Furniture loans $__________ Other secured loans $__________ Signature loans $__________ Risk-free securities $___________ What is the projected total annual return? Annual Return = $____________