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used to your score. 1. (-/3 Points DETAILS TANAPMATH7 6.2.001 MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Formulate but do not solve the following exercise as a linear plogramming problem A company marafactures x units of Product and y units of Product 8, on two machines, I and II. It has been determined that the company will realize a profit of ston nach unit of Product A and 53 on each unit of Product B. To manufacture a unit of Product Arequires 5 min on Machine andmin on Machine Il. To manufacture a unit of Product requires 9 min on Machine 1 and 4 min on Machine II. There are 206 min wallable on Machine and 144 min available on Machine I in each work shit. How many units of a product should be produced in each shift to maximize the company's profit in daar? Maximize P subject to the constraints Machine Machine Formulate but do not solve the following exercise as a linear programming problem. National Business Machines manufactures two models of portable printers: A and B. Each model A costs $110 to make, and each model B costs $150. The profits are $25 for tach model A and $25 for each model B portable printer. If the total number of portable printers demanded per month does not exceed 2500 and the company has carmarked not more than $500,000/month for manufacturing costs, how many units of each model should National make each month to maximize its monthly profits Pin dollars? (Let x represent the number of units of model A and y represent the number of units of model s.) Maximize subject to the constraints manufacturing costs number produced X20 y20 EACHER PRACTICE ANOTI Formulate but do not solve the following exercise as a linear programming problem, Kane Manufacturing has a division that produces two models of fireplace grates, x units of model A and y units of model B. To produce each model A requires 3 lb of cast and 7 min of labor. To produce each model B grate requires 4 tb of cast iron and 5 min of labor. The profit for each model A grate is $2.50, and the profit for each model B grate is $2.00, 1400 tb of cast iron and 1200 min of labor are available for the production of grates per day, Because of a backlog of orders on model A grates, the manager of Kare Manufacturing has decided to produce at least 150 of these grates a day. Operating under this additional constraint, how many grates of each model should Kane produce to maximize profit Pin dollars? Maximize subject to the constraints cast iron labor model A YO Formulate but do not solve the following exercise as a linear programming problem A division of the Winston Furniture Company manufactures x dining tables and y chairs. Each table requires 40 board feet of wood and 3 labor hours. Each chair requires 10 board feet of wood and 4 labor hours. In a certain vie, the company has 1200 board Font of wood available and 540 labor hours. ll the proft for each table is $50 and the profit for each chair is $18, how many tables and chairs should Winston manufacture to maximize its profits Pin dollars? P- subject to the contents Maximize board feet Labor-hour 20 YO Formulate but do not solve the following exercise as a linear programming problem Madison Finance has a total of $16 milion earmarked for homeowner loans and autoloans, where x'is homeowner loans in millions of dollars and y is auto loans in milions of dollars. On the average, homeowner loans have a 10 annual rate of return, whereas auto loans yield a 12 annual rate of return. Management has also stipulated that the total amount of homeowner loans should be greater than or equal to 4 times the total amount of automobilelona. Determine the total amount of loans of each type Madison should extend to each category to maximize its returns Pin millions of dollars Mawie subject to the constraints Stallons on of loans 720 Formulate but do not solve the following exercise as a inear programming problem. A farmer plans to plant two crops. A and B. The cost of cultivating Crop As $30/acre, whereas the cost of cultivating Crop 8 is $70/acre. The farmer has a maximum of 57300 available for land cultivation. Each acre of Crop Arequires 20 labor hours, and each acre of Crep requires 25 labor hours. The farmer has a maximum of 3400 Sabar-hours wailable. If she expects to make a profit of $150/acre on Crop Aand 230/acre on Crop , how many acres of each crop, and respectively, should the blant to maximize her profit Pin dollars? Marie P- subject to the constraints cost Isbar X2 Y20 Formulate but do not solve the following exercise as a linear programming problem. Deluxe River Cruises operates a fleet of river vessels. The feet has two types of vessels A type A vessel x, has 40 deluxe cabins and 165 standard cabins, whereas a type vessel, y, has 70 deluxe cabins and 115 standard cabins. Under a charter agreement with Odyssey Travel Agency, Deluxe River Cruises is to provide Odyssey with a minimum of 350 deluxe and 660 standard cabins for their 15-day cruise in May. It costs $49,000 to operate a type A vessel and $57,000 to operate a type B vessel for that period. How many of each type of vessel should be used in order to keep the operating costs, in dollars), to a minimum? Minimize CE subject to the constraints deluxe cabins standard cabins *20 720 Formulate but do not solve the following exercise as a linear programming problem, A company manufactures x units of product A y units of product 8, and 2 units of product C. Each product is processed in three departments: I, II, and IT. The total available labor-hours per week for Departments I, II and III are 860, 1940, and 840, respectively. The time requirements (in hours per unit) and profit per unit for each product are as follows. Dept. 1 Dept. II Dept. III Profit Product 2 3 2 $16 Product B 1 1 2 $10 Product c 2 2 1 $14 How many units of each product should the company produce in order to maximize its profit. Pin dollars? subject to the constraints Maximize PE Department1 Department 11 Department in 20 20