Blue Ridge Hot Tubs manufactures and sells two models of hot tubs: the Aqua-Spa and the Hydro-Lux. Howie Jones, the owner and manager of the company, needs to decide how many of each type of hot tub to produce during his next production cycle. Howie buys prefabricated fiberglass hot tub shells from a local supplier and adds the pump and tubing to the shells to create his hot tubs. (This supplier has the capacity to deliver as many hot tub shells as Howie needs.) Howie installs the same type of pump into both hot tubs. He will have only 200 pumps available during his next production cycle. From a manufacturing standpoint, the main difference between the two models of hot tubs is the amount of tubing and labor required. Each Aqua-Spa requires 9 hours of labor and 12 feet of tubing. Each Hydro-Lux requires 6 hours of labor and 16 feet of tubing. Howie expects to have 1,566 production labor hours and 2,880 feet of tubing available during the next production cycle. Howie earns a profit of $340 on each Aqua-Spa he sells and $290 on each Hydro-Lux he sells. He is confident that he can sell all the hot tubs he produces. The production of each Aqua-Spa generates 15 pounds of a toxic resin, whereas each Hydro-Lux produces 10 pounds of toxic resin. Howie has identified two different objectives that could apply to his problem: He can maximize profit or he can minimize the production of toxic resin. Suppose Howie considers the maximization of profit as half as important as the minimization of toxic resin. (Let X₁ be the number of Aqua-Spa hot tubs produced and let X2 be the number of Hydro-Lux hot tubs produced. Use a weight of 1 for the profit objective.) (a) Formulate an MOLP model for Howie's decision problem. MIN: Subject to: profit (in dollars) 340x1 +290x2 + .5(W1+ W2) SQ toxic resin (in pounds) 15x1 +10x2 ≤ Q pumps 1x₁ + 1x2 ≤200 labor (in hours) 9x1 + 6x2 <1566 tubing (in ft) X1, X2 20 (b) Implement your model in a spreadsheet and solve it. What is the solution to Howie's MOLP problem? (Round your answers to the nearest integer.) (X1, X2)=122,78 This is an MOLP model. To formulate the model, you must first solve an LP model for each individual objective. Do not add integer constraints for this problem.

Blue Ridge Hot Tubs manufactures and sells two models of hot tubs: the Aqua-Spa and the Hydro-Lux. Howie Jones, the owner and manager of the company, needs to decide how many of each type of hot tub to produce during his next production cycle. Howie buys prefabricated fiberglass hot tub shells from a local supplier and adds the pump and tubing to the shells to create his hot tubs. (This supplier has the capacity to deliver as many hot tub shells as Howie needs.) Howie installs the same type of pump into both hot tubs. He will have only 200 pumps available during his next production cycle. From a manufacturing standpoint, the main difference between the two models of hot tubs is the amount of tubing and labor required. Each Aqua-Spa requires 9 hours of labor and 12 feet of tubing. Each Hydro-Lux requires 6 hours of labor and 16 feet of tubing. Howie expects to have 1,566 production labor hours and 2,880 feet of tubing available during the next production cycle. Howie earns a profit of $340 on each Aqua-Spa he sells and $290 on each Hydro-Lux he sells. He is confident that he can sell all the hot tubs he produces. The production of each Aqua-Spa generates 15 pounds of a toxic resin, whereas each Hydro-Lux produces 10 pounds of toxic resin. Howie has identified two different objectives that could apply to his problem: He can maximize profit or he can minimize the production of toxic resin. Suppose Howie considers the maximization of profit as half as important as the minimization of toxic resin. (Let X₁ be the number of Aqua-Spa hot tubs produced and let X2 be the number of Hydro-Lux hot tubs produced. Use a weight of 1 for the profit objective.) (a) Formulate an MOLP model for Howie's decision problem. MIN: Subject to: profit (in dollars) 340x1 +290x2 + .5(W1+ W2) SQ toxic resin (in pounds) 15x1 +10x2 ≤ Q pumps 1x₁ + 1x2 ≤200 labor (in hours) 9x1 + 6x2 <1566 tubing (in ft) X1, X2 20 (b) Implement your model in a spreadsheet and solve it. What is the solution to Howie's MOLP problem? (Round your answers to the nearest integer.) (X1, X2)=122,78 This is an MOLP model. To formulate the model, you must first solve an LP model for each individual objective. Do not add integer constraints for this problem.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.1: Systems Of Equations

Problem 25E

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