Investigacion Operaciones
Tarea 1
Instrucciones. Resolver los siguientes problemas.
Problema 1 (extraído del libro de texto, modificado problema 2, página 55)
Farmer Jones must determine how many acres of corn and wheat to plant this year. An acre of wheat yields 25 bushels of wheat and requires 10 hours of labor per week. An acre of corn yields 10 bushels of corn and requires 4 hours of labor per week. All wheat can be sold at $4 a bushel, and all corn can be sold at $3 a bushel. Seven acres of land and 40 hours per week of labor are available. Government regulations require that at least 30 bushels of corn be produced during the current year. Let x1 = number of acres of corn planted, and x2= number of acres of wheat planted. a. Using these decision variables formulate an LP whose solution will tell Farmer Jones how to maximize the total revenue from wheat and corn. b. Is (x1 = 2, x2 = 3) in the feasible region? c. Is (x1 = 4, x2 = 3) in the feasible region? d. Is (x1 = 2, x2 = _1) in the feasible region? e. Is (x1 = 3, x2 =2) in the feasible region?
Problema 2 (extraído del libro de texto, problema 8, página 68)
Graphically find all optimal solutions to the following LP:
Min z = x1 - x2 s.t. x1 + x2 ≤ 6 x1 - x2 ≥ 0 x2 - x1 ≥ 3 x1, x2 ≥ 0.
Problema 3 (extraído del libro de texto, problema 10, página 115)
Carco has a $150,000 advertising budget. To increase automobile sales, the firm is considering advertising in newspapers and on television. The more Carco uses a particular medium, the less effective is each additional ad. Table 50 shows the number of new customers reached by each ad. Each newspaper ad costs $1,000, and each television ad costs $10,000. At most, 30 newspaper ads and 15 television ads can be placed. How can Carco maximize the number of new customers created by advertising?
Problema 4 (extraído del libro de texto, problema 17, página 115)
Furnco manufactures tables and chairs. Each table and chair must be made entirely out of oak or entirely out of pine. A total of 150
Instrucciones. Resolver los siguientes problemas.
Problema 1 (extraído del libro de texto, modificado problema 2, página 55)
Farmer Jones must determine how many acres of corn and wheat to plant this year. An acre of wheat yields 25 bushels of wheat and requires 10 hours of labor per week. An acre of corn yields 10 bushels of corn and requires 4 hours of labor per week. All wheat can be sold at $4 a bushel, and all corn can be sold at $3 a bushel. Seven acres of land and 40 hours per week of labor are available. Government regulations require that at least 30 bushels of corn be produced during the current year. Let x1 = number of acres of corn planted, and x2= number of acres of wheat planted. a. Using these decision variables formulate an LP whose solution will tell Farmer Jones how to maximize the total revenue from wheat and corn. b. Is (x1 = 2, x2 = 3) in the feasible region? c. Is (x1 = 4, x2 = 3) in the feasible region? d. Is (x1 = 2, x2 = _1) in the feasible region? e. Is (x1 = 3, x2 =2) in the feasible region?
Problema 2 (extraído del libro de texto, problema 8, página 68)
Graphically find all optimal solutions to the following LP:
Min z = x1 - x2 s.t. x1 + x2 ≤ 6 x1 - x2 ≥ 0 x2 - x1 ≥ 3 x1, x2 ≥ 0.
Problema 3 (extraído del libro de texto, problema 10, página 115)
Carco has a $150,000 advertising budget. To increase automobile sales, the firm is considering advertising in newspapers and on television. The more Carco uses a particular medium, the less effective is each additional ad. Table 50 shows the number of new customers reached by each ad. Each newspaper ad costs $1,000, and each television ad costs $10,000. At most, 30 newspaper ads and 15 television ads can be placed. How can Carco maximize the number of new customers created by advertising?
Problema 4 (extraído del libro de texto, problema 17, página 115)
Furnco manufactures tables and chairs. Each table and chair must be made entirely out of oak or entirely out of pine. A total of 150