Question

Joe is using the function E= 1.89x + 2.89y to minimize his expenses when selling

markers and erasers. He has the following
constraints.
2x + y > 10
x + 2y > 8
X>0
y >
What is the minimum value of E?
$28.90
$9.45
$15.12
$13.34

Answer 1

`(d)\ \$13.34`

Explanation:

Given

`E = 1.89x + 2.89y` -- Objective function

Constraints:

`2x + y > 10`

`x + 2y > 8`

`x,y>0`

Required

Minimum value of E

To do this, we apply graphical method

See attachment for plots of
`2x + y > 10` and
`x + 2y > 8`

From the attached plot, the point that satisfy
`x,y>0` is:

`(x,y) = (4,2)`

So, we have:

`E = 1.89x + 2.89y`

This gives:

`E =1.89 * 4 + 2.89 * 2`

`E =7.56 + 5.78`

`E =13.34`