A Concise Intro To Logic
12th Edition
ISBN: 9781305147775
Author: Hurley
Publisher: Cengage
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The person says that 2173 is a prime number because it ends in the number3, and since 3 is a prime number then that means that 2173 is a prime number. Is2173 a prime number? What can you conclude about this person’s reasoning? Explain your answer.
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In Simplex Method, the pivot element should be changed to 1 in the formulation of the next table.
Use the simplex method to maximize the given function. Assume all variables are nonnegative.
Maximize
f = 20x + 12y + 12z
subject to the following.
x
+
z
≤
45
x
+
y
≤
30
y
+
z
≤
45
(x,y,z)=
f=
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- A company manufactures two products. If it chargesprice pi for product i, it can sell qi units of product i,where q1 = 60 - 3p1 + p2 and q2 = 80 - 2p2 + p1. Itcosts $5 to produce a unit of product 1 and $12 to produce a unit of product 2. How many units of eachproduct should the company produce, and what pricesshould it charge, to maximize its profit? Use spreadsheet modelling in Excelarrow_forward1. A company produces three different products; x,y, and z. For the production of 1 unit of product x, 1 unit of A and 1 unit of B are used as input. 1 unit of A and 2 units of B are used to produce 1 unit of product y. To produce 1 unit of product z, only 1 unit of A is used. The company holds 40 units of A and 20 units of B periodically in total. By the way, the company can not produce product y more than the twice of product z. On the other hand, the sale price of 1 unit of product x is 10 TL, product y is 15 TL and product z is 12 TL. Furthermore, the cost of 1 unit of product x is 8 TL, product y is 9 TL and product z is 7 TL. According to above information, what should be the company’s optimal product mix to maximize its profit? Construct the problem as a LP model. 2. Solve the above problem by using Simplex Method. 3. Min Z = 0.4 x1 + 0.5 x2 Subject to 0.3 x1 +0.1 x2 ≤ 2.7 0.5x1 +0.5x2 = 6 0.6 x1 + 0.4x2 ≥ 6 x1 - 2x2 ≥ 0 x1, x2 ≥ 0 Create a problem and define the decision…arrow_forwardThere are 2657 professors in a college out of which one ofthem has to be selected for promotion through a game.Everyone will sit in a circle with numbered chairs. Each ofthem will evict the professor to his left, starting from the firstchair, and this cycle will go on until one last professor is left.Now you are one of the professors, which chair would youpick to ensure you get promoted?arrow_forward
- What inverse operations is used to solve equations 2x=10arrow_forwardUse the simplex method to maximize the given function. Assume all variables are nonnegative.Maximize f = 3x + 22y subject to 14x + 7y ≤ 35 5x + 5y ≤ 50 (x,y)= f=arrow_forwardA company produces three different products; x,y, and z. For the production of 1 unit of product x, 1 unit of A and 1 unit of B are used as input. 1 unit of A and 2 units of B are used to produce 1 unit of product y. To produce 1 unit of product z, only 1 unit of A is used. The company holds 40 units of A and 20 units of B periodically in total. By the way, the company can not produce product y more than the twice of product z. On the other hand, the sale price of 1 unit of product x is 10 TL, product y is 15 TL and product z is 12 TL. Furthermore, the cost of 1 unit of product x is 8 TL, product y is 9 TL and product z is 7 TL. According to above information, what should be the company’s optimal product mix to maximize its profit? Construct the problem as a Linear programming model. Solve the above problem by using Simplex Method.arrow_forward
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