QUESTION 1 Muir Manufacturing produces two popular grades of commercial carpeting among its many other products. In the coming production period, Muir needs to decide how many rolls of each grade should be produced in order to maximize profit. Each roll of Grade X carpet uses 50 units of synthetic fiber, requires 25 hours of production time, and needs 20 units of foam backing. Each roll of Grade Y carpet uses 40 units of synthetic fiber, requires 28 hours of production time, and needs 15 units of foam backing The profit per roll of Grade X carpet is $200, and the profit per roll of Grade Y carpet is $160. In the coming production period, Muir has 3000 units of synthetic fiber available for use. Workers have been scheduled to provide at least 1800 hours of production time (overtime is a possibility). The company has 1500 units of foam backing available for use. Develop and solve a linear programming model for this problem QUESTION 2 Evans Enterprises bought a prime parcel of beachfront property and plans to build a luxury hotel on it. After meeting with the architectural team, the Evans family 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 the four kinds of rooms to plan for, the Evans family will consider the following information: 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. a. b. Construction costs vary. The cost estimate is $12,000 for a lagoon view room and $15,000 for a beachfront room. 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. There will be at least 100 but no more than 180 beachfront rooms. 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. C. d. Industry trends recommend that the number of smoking rooms be no more than 50% of the number of non-smoking rooms. e. Develop the linear programming model to maximize revenue