Note this question is continued on the nert Please free both

Note: this question is continued on the nert Please free both pages to answer part (c). Consider the following linear programming problem: maximize the the objective function f T y) 4y subject to 12r 5y S 200 2I 5y S 100 I 20 (a) Rewrite the first two inequalities as equations with slack variables. Include any constraints to which those slack variables are subject. (b) Construct the initial simplex tableau for this linear programming problem. (c) Use the simplex method to determine the maximum value of f (I,y)

Solution

given equations are

x>=0

y>=0

12x+5y<=200

2x+5y<=100

by drawing all the given equations on the graph

we get the vertices of the closed polygon

vertices are (0,0),(50,0),(0,40),(10,18)

we get maximum value at the vertex (0,40) and the maximum value is 2x+4y=2*0+4*40=160