Question

Find the optimal solution for the following problem. (Round your answers to 3 decimal places.)

Minimize C =	5x + 11y
subject to	4x + 6y ≥ 13
	7x + 4y ≥ 13
and	x ≥ 0, y ≥ 0.

1. What is the optimal value of x?

2. What is the optimal value of y?

3. What is the minimum value of the objective function?

Answer 1

a)optimal vaule of x is 1

solution:

given equations: 4x+6y>or=13 , 7x+4y>or=13

to get optimal value [here minimum value] we use equations,

4x+6y=13 and 7x+4y=13

6y=13-4x and 4y=13-7x : [solving the equation]

y=(13-4x)/6 and y=(13-7x)/4

that means, (13-4x)/6 = (13-7x)/4

cross multiply 6 and 4

(13-4x)*4 = (13-7x)*6

52-16x = 78-42x

taking x variable into one side we get

42x-16x = 78-52

26x = 26

x=1

by solving this equation we got the omtimal value of x as 1.

b)optimal value of y is 1.5

solution:

by solving the above equations 4x+6y= 13 and 7x+4y=13,

we got x=1

giving the value of x as 1

we get 4*1+ 6y=13

6y=13-4=9

y=9/6

=1.5 [ or else we can find y by solving the above equation directly as well]

c) we have got optimal value[minimal value] of x=1 and y=1.5

giving the values of x and y in the objective function c=5x+11y we get

c= (5*1)+ (11*1.5)

c= 5 + 16.5

c= 21.5

that means the minimum value of objetive funtion is 21.5