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page%2063 - PHUELEMS Group A'l Graphically solve Problem I...

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Unformatted text preview: PHUELEMS Group A 'l Graphically solve Problem I of Section 3.1. 2; Graphically solve Problem 4 of Section 3.1. 3 Leary Chemical manufactures three chemicals: A. B. and C. These chemicals are produced via two production processes: 1 and 2. Running process 1 for an hour costs $4 and yields 3 units ol‘A, l of B, and l of C. Running process 2 for an hour costs Si and produces l unit ofA and l of B. To meet customer demands, at least l0 units ofA, 5 of B, and 3 of C must be produced daily. Graphically determine a daily production plan that minimizes the cost of meeting Leary Chemicals daily demands. 4 For each of the following, determine the direction in which the objective function increases: it 2 = 4x, w x2 i] I ‘itl + 2x; I.“ 2' : mx, — 3x3 f] 5 Furnco manufactures desks and chairs. Each desk uses 4 units of wood, and each chair uses 3. A desk contributes 3.3 Special Cases 540 to profit. and a chair contributes $25. Marketing restrictions require that the number of chairs produced be at least twice the number of desks produced. ['1’ 20 units of wood are available, formulate an LP to maximize Furnco’s profit, Then graphicaliy solve the LP. E Farmer éane owns 45 acres of land. She is going to plant each with wheat or corn. Each acre planted with wheat yieids $200 profit; each with corn yields $300 profit. The labor and fertilizer used for each acre are given in Tabie 1. One hundred workers and 120 tons of fertilizer are available. Use linear programming to determine how Jane can maximize profits from her land. "tn is L a “t WW WWir—aii" " WWEZEJW Labor 3 workers 2 workers 2 tons 4 tons The Giapetto and Borian problems each had a unique optimal solution. in this section, we encounter three type of LPs that do not have unique optimai solutions. i Sonic LPs have an infinite number of optimal solutions {alternative or multiple opti— mal solutions). 3 Some Ll’s have no feasibie solutions (infecrsibi'e LPs). 3 Some Li’s are unbounded: There are points in the feasible region with arbitrarily large (in a max problem) z—values. sitter-native or tittettipte @pttmai Eotuttons E XAMPL E 3 ‘ An auto company manufactures cars and trucks. Each vehicle must be processed in the paint shop and body assembly shop. If the paint shop were only painting trucks, then 40 per day could be painted. If the paint shop were only painting cars, then 60 per day could be painted. if the body shop were only producing cars, then it could process 50 per day. if the body shop were only producing, trucks. then it could process 50 per day. Each truck contributes $300 to profit, and each car contributes $200 to profit. Use linear program- ming to determine a daily production schedule that will maximize the company’s profits. Solution The company must decide how many cars and trucks should be produced daily. This leads us to define the foliowing decision variables: x1: X2: number of trucks produced daily number of cars produced daiiy 3 . 3 Sandal Eases $3 ...
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