Problem 1 Wes Wheeler is the production manager of Wheeler Wheels, Inc. Wes has just received orders for 1,000 standard wheels and 1,250 deluxe wheels next month and for 800 standard and 1,500 deluxe wheels the following month. All orders are to be filled. The cost of producing standard wheels is $10 and deluxe wheels is $16. Overtime rates are 50% higher. There are 1,000 hours of regular time and 500 hours of overtime available each month. It takes .5 hour to make a standard wheel and .6 hour to make a deluxe wheel. The cost of storing one wheel from one month to the next is $2. Wes wants to develop a two-month production schedule for standard and deluxe wheels. Formulate this production planning problem as a linear program.

Problem 2 Winslow Savings has $20 million available for investment. It wishes to invest over the next four months in such a way that it will maximize the total interest earned over the four-month period as well as have at least $10 million available atthe start of the fifth month for a high-rise building venture in which it will be participating. For the time being, Winslow wishes to invest only in 2-month government bonds (earning 2% over the 2-month period) and 3-month construction loans (earning 6% over the 3-month period). Each of these is available each month for investment. Funds not invested in these two investments are liquid and earn 3/4 of 1% per month when invested locally. Formulate a linear program that will help Winslow Savings determine how to invest over the next four monthsif at no time doesit wish to have more than $8 million in either government bonds or construction loans.

Problem 3 BP Cola must decide how much money to allocate for new soda and traditional soda advertising over the coming year. The advertising budget is $10,000,000. Because BP wants to push its new sodas, at least one-half of the advertising budget is to be devoted to new soda advertising. However, at least $2,000,000 is to be spent on itstraditional sodas. BP estimates that each dollarspent on traditional sodas will translate into 100 canssold, whereas, because of the hardersell needed for new products, each dollar spent on new sodas will translate into 50 cans sold. To attract new customers BP has lowered its profit margin on new sodas to 2 cents per can as compared to 4 cents per can for traditional sodas. How should BP allocate its advertising budget if it wants to maximize its profits while selling at least 750 million cans? Formulate and solve a linear program to answer what is asked.

Problem 4 Evans Enterprises has bought a prime parcel of beachfront property and plans to build a luxury hotel. After meeting with the architectural team, the Evansfamily has drawn up some information to make preliminary plans for construction. Excluding the suites, which are not part of this decision, the hotel will have four kinds of rooms: beachfront non-smoking, beachfront smoking, lagoon view non-smoking, and lagoon view smoking. To decide how many of each of the four kinds of rooms to plan for, the Evans family will consider the following information.

a) After adjusting for expected occupancy, the average nightly revenue for a beachfront non-smoking room is $175. The average nightly revenue for a lagoon view non-smoking room is $130. Smokers will be charged an extra $15.

b) Construction costs vary. The cost estimate for a lagoon view room is $12,000 and for a beachfront room is $15,000. Air purifying systems and additional smoke detectors and sprinklers ad $3000 to the cost of any smoking room. Evans Enterprises has raised $6.3 million in construction guarantees for this portion of the building.

c) There will be at least 100 but no more than 180 beachfront rooms.

d) Design considerations require that the number of lagoon view rooms be at least 1.5 times the number of beachfront rooms, and no more than 2.5 times that number.

e) Industry trends recommend that the number of smoking rooms be no more than 50% of the number of non-smoking rooms. Develop the linear programming model to maximize revenue.