Question

In: Accounting

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

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?
  1. What is the optimal value of y?
  1. What is the minimum value of the objective function?

Solutions

Expert Solution

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


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