Question

Find the values of x and y that maximize the objective function x + 4y for the feasible set in the figure below. Ay (0,4) feasible set (0,0) (5,2) (6,0). find the value of x and y.

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Answer 1

x = 0,y = 4

explanation :

just plug in the value of x and y from each set in the function and compare which one gives the greatest value.

for (0,0) : x + 4y = 0 + 4(0) = 0

for (6,0) : x + 4y = 6 + 4(0) = 6

for (5,2) : x + 4y = 5 + 4(2) = 13

for (0,4) : x + 4y = 0 + 4(4) = 16

from the above values, we can collect that at point (0,4), the value of objective function x +4y is maximum.

Answer 2

x = 0

y = 4

Explanation:

The feasible region is the set of all possible solutions that satisfy a given set of constraints in a mathematical optimization problem.

The given feasible region, determined by a set of constraints, has four vertices (corner points):

• (0, 0)
• (0, 4)
• (5, 2)
• (6, 0)

To determine the values of x and y that maximize the objective function x + 4y, substitute the x and y values of the corner points into the function and calculate the resulting objective function values. The result that is the maximum is the

`(0, 0)\implies (0)+4(0)=0`

`(0, 4)\implies (0)+4(4)=16`

`(5,2)\implies (5)+4(2)=13`

`(6, 0)\implies (6)+4(0)=6`

The maximum is the vertex (0, 4), where the objective function yields the highest value of 16. Therefore, the values of x and y that maximize the objective function:

• 
  `x = 0`
• 
  `y = 4`