Consider the following linear programming problem: Maximize 12X + 10Y Subject to: 4X + 3Y ≤ 480 2X + 3Y ≤ 360 all variables ≥ 0 The maximum possible value for the objective function is __________.
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Consider the following linear programming problem:
Maximize 12X + 10Y
Subject to:
4X + 3Y ≤ 480
2X + 3Y ≤ 360
all variables ≥ 0
The maximum possible value for the objective function is __________.
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- . Consider the following linear programming problem: Maximize 12X + 10Y Subject to: 4X + 3Y = 480 2X + 3Y 360 all variables 20 Which of the following points (X,Y) is not feasible? a (70,70) b. (20,90) c. (100,10) d. (0,100) كلا أجرب الأرقام بالـؤالApply Linear Programming to the Folling Question: Dan Reid, chief engineer at New Hampshire Chemical, Inc., has to decide whether to build a new state-of-art processing facility. If the new facility works, the company could realize a profit of $200,000. If it fails, New Hampshire Chemical could lose $150,000. At this time, Reid estimates a 60% chance that the new process will fail. The other option is to build a pilot plant and then decide whether to build a complete facility. The pilot plant would cost $10,000 to build. Reid estimates a fifty-fifty chance that the pilot plant will work. If the pilot plant works, there is a 90% probability that the complete plant, if it is built, will also work. If the pilot plant does not work, there is only a 20% chance that the complete project (if it is constructed) will work. Reid faces a dilemma. Should he build the plant? Should he build the pilot project and then make a decision? Help Reid by analyzing this problemYou are to set up a linear program
- Solve the following Linear Programming model using the graphical method (USING EXCEL){Write the steps of construction} Q1)MaximizeH = x + 3y Objective functionsubject tox + y ≤ 502x + y ≤ 60 x ≥ 0, y ≥ 0For the remaining questions, consider the following problem description: An oil company is considering exploring new well sites S₁, S2, ..., S10 with respective costs C1, C2, C10. And in particular they want to find the least-cost selection of 5 out of the 10 possible sites. The binary decision variables x₁,x2,..., X10 denote the decision to explore the corresponding site.Solve the following linear programming problem. Maximize: z=6x + 14y subject to: 7x+3y ≤21 9x+y≤21 x20, y 20 The maximum value is The maximum occurs at the point (Type an ordered pair. If the maximum occurs at more than one point, type either answer. Type an integer or a fraction.)
- A college student works in both the school cafeteria and library. She works no more than 12 hours per week at the cafeteria, and no more than 16 hours per week at the library. She must work at least 20 hours each week. Write a system of inequalities that describes all the given conditions. Write a system of inequalities letting x= number of hours worked at the cafeteria per week and y = number of hours worked at the library per week. x+yz x≤ ysConsider the following LP problem: Min 6X+ 27Y Subject to : 2 X + 9Y => 25, and X + Y <= 75. Pick a suitable statement for this problem: a. X=37.5, Y=37.5 is the only optimal solution. b. Optimal Obj. function value is 75 c. X = 0, Y = 0 is the only optimal solution. d. Optimal Obj. function value is 0Facility Location. A paper products manufacturer has enough capital to build and manage some additional manufacturing plants in the United States in order to meet increased demand in three cities: New York City, NY; Los Angeles, CA; and Topeka, KS. The company is considering building in Denver, CO; Seattle, WA; and St. Louis, MO. Max Operating Capacity 400 tons/day 700 tons/day Denver Seattle $10/ton $17/tor $5/ton $11/ton.... $18/ton.... $28/ton Los Angeles Topeka New York City Figure 1: Graphical representation of the given data = • The cost fi of building plants in these cities is fi $10,000,000 in Seattle. Unmet Demand 300 tons/day 100 tons/day 500 tons/day • Due to geographic constraints, plants in Denver and Seattle would have a maximum operating capacity kį of 400 tons/day and 700 tons/day respectively. $5,000,000 in Denver and f2 = • The cost cij per ton of transporting paper from city i to city j is outlined in Figure 1. • The unmet demand d, for Los Angeles, Topeka, and New…
- A group of students organizes a bake sale in which they sell hundreds of cookies at$1 per piece. They set up a table on campus and wait for students to come and purchasetheir cookies. Consider the following variables in this bake sale operation:1. Size of the cookies2. Weather conditions on campus3. Organization of the table4. Number of cookies sold5. Competition from other fund-raisers coinciding on campus6. Amount of advertising and shouting of the students at the bake sale table7. Number of students on campus that dayWhich of these variables are input variables?a. 1 and 2b. 1 and 3c. 1, 3, and 5d. 1, 3, and 6What combination of x and y will yield the optimum for this problem? Maximize Z = $3x + $15y Subject to: Multiple Choice x= 0, y=4 x= 0, y=3 x= 0, y=0 x= 2y=0 O x=1,y=25 2x + 4y ≤ 12 5x + 2y ≤ 10Consider the following Pareto maximization problem with decision variables x and y: vmax (x2 + x, - 2y) s.t. 0< x< 10 0< y< 5. What is the unique efficient point for this problem? (0,0) (10,5) (10,0) (110,0)