Find the values of x1 and x2 where the following two constraints intersect. (Round your answers to 3 decimal places.) (1) 10x1 + 5x2 ≥ 50 (2) 1x1 + 2x2 ≥ 12
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Find the values of x1 and x2 where the following two constraints intersect. (Round your answers to 3 decimal places.)
-
(1) 10x1 + 5x2 ≥ 50
-
(2) 1x1 + 2x2 ≥ 12
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- Find the values of x1 and x2 where the following two constraints intersect. (Round your answers to 3 decimal places.) (1) 10x1 + 5x2 ≥ 50 (2) 1x1 + 2x2 ≥ 12For the products A, B, C, and D, which of the following could be a linear programming objective function? Select one: a. Z = 1A + 2BC + 3D b. Z = 1A + 2AB + 3ABC + 4ABCD c. Z = 1A + 2B + 3C + 4D d. Z = 1A + 2B/C + 3DVladimir Ulanowsky is playing Keith Smithson in atwo-game chess match. Winning a game scores 1 match 19.4 Further Examples of Probabilistic Dynamic Programming Formulations 1029 point, and drawing a game scores 12match point. After thetwo games are played, the player with more match points isdeclared the champion. If the two players are tied after twogames, they continue playing until someone wins a game(the winner of that game will be the champion). Duringeach game, Ulanowsky can play one of two ways: boldly orconservatively. If he plays boldly, he has a 45% chance ofwinning the game and a 55% chance of losing the game. Ifhe plays conservatively, he has a 90% chance of drawing thegame and a 10% chance of losing the game. Ulanowsky’sgoal is to maximize his probability of winning the match.Use dynamic programming to help him accomplish thisgoal. If this problem is solved correctly, even thoughUlanowsky is the inferior player, his chance of winning the match is over 12. Explain this…
- XYZ Inc. produces two types of paper towels, called regular and super-soaker. Regular uses 2 units of recycled paper per unit of production and super-soaker uses 3 units of recycled paper per unit of production. The total amount of recycled paper available per month is 10,000. Letting X1 be the number of units of regular produced per month and X2 represent the number of units of super-soaker produced per month, the appropriate constraint/s will be ___________ a. 2X1 = 3X2 b. 2X1 + 3X2 ≥ 10000 c. 2X1 + 3X2 = 10000. d. 2X1 + 3X2 ≤ 1000Use the simplex method to solve. Maximize z = 4x1 + 2x2, subject to 3x1 + x2 < 22 3x1 + 4x2 < 34 x1 > 0, x2 > 0 x1 = x2 = x3 =Analyze algebraically what special case in simplex application is present in each of the LP model below. Give an explanation to support your answer. a) Maximize z = 4x1 + 2x2 Subject to: 2x1 - x2 ≤ 2 3x1 - 4x2 ≤ 8 x1, x2 ≥ 0b) Maximize z = 3x1 + 2x2 Subject to: 4x1 - x2 ≤ 8 4x1 + 3x2 ≤ 12 4x1 + x2 ≤ 8 x1, x2 ≥ 0
- Consider the given LP:Maximize z = 4x1 + 6x2 + 8x3Subject to 3x1 + 2x2 + 5x3<= 30 9x1 + 2x2 + 7x3 <= 126 2x1 + 3x2 + x3<= 60 xi>= 01-Find the optimal values of Z, x1, x2, x3 by using the simplex method.3-If the RHS of the constraint 1 is 34 instead of 30, what is the new value of Z?Suppose you own 11 bronze coins worth a total of $150,11 silver coins worth a total of $160, and 11 gold coinsworth a total of $170. Develop a linear integer model tofind a combination of coins worth exactly $110Consider the following LP problem developed at Zafar Malik's Carbondale, Illinois, optical scanning firm: Maximize Z= 1X1+1X2 Subject to: 2X1+1X2≤100 (C1) 1X1+2X2≤100 (C2) X1,X2≥0 Part 2 The optimum solution is: Part 3 X1= ______ (round your response to two decimal places).
- The cost per day of running a hospital is 200,000 +0.5x2 dollars, where x is the number of patients served per day. What number of patients served per day minimizes the cost per patient per day of running thehospital if the hospital’s daily capacity is 300 patients? How does the solution change as the hospital’s capacity increases? Let capacity increase from 300 to500 in increments of 25.Solve Maximize: Z = 4X1 + 3X2 + 9X3 Subject to: 2X1 + 4X2 + 6X3 ≥ 15 6X1 + X2 + 6X3 ≥ 12 X1, X2, X3 ≥ 0 Use simplex method.