Question: 1. Find the optimal value by Simplex method with Pivot operation (2 point) MaximizeSubjecttoZ=2x1+x22x1x28x1+2x214x1+x24x1,x20 2. Find the optimal value by Simplex method with Slack variables

1. Find the optimal value by Simplex method with
1. Find the optimal value by Simplex method with Pivot operation (2 point) MaximizeSubjecttoZ=2x1+x22x1x28x1+2x214x1+x24x1,x20 2. Find the optimal value by Simplex method with Slack variables ( 2 point) MinimizeSubjecttoZ=600x1+500x22x1+x280x1+2x260x1,x20 3. The Happy company is experimenting with three types of network modules P,Q, and R in which three kinds of functions which are A, B, and C. Taking the various factors into account, it has been decided to use the maximum 600 routers of functions A, maximum 480 routers of functions B and maximum 540 routers of function C. Network P requires 3, 2, 2 routers, network Q requires 1,4,3 routers and network R requires 4,2,3 routers of functions A,B and C respectively. Network module P is estimated to give a profit of 2-million-baht, Network module Q. a profit of 3 million baht, and Network module R, a profit of 4 million baht, respectively. Finding the maximum profit and optimum points? (Using the Simplex method with slack variables) (3 point) 4. Consider the Linear Programming as follow: MaximizeSubjecttoz=5x+4y6x+4y24x+2y6x+y1y2x0y0(1)(2)(3)(4)(5)(6) a. What is feasible region of this question? ( 1 point) b. Find all coordinate points for the above feasible region with their results? (1.5 points) c. What is the optimal value in this objective function? ( 0.5 points)

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