Answer:
[tex](d)\ \$13.34[/tex]
Step-by-step explanation:
Given
[tex]E = 1.89x + 2.89y[/tex] -- Objective function
Constraints:
[tex]2x + y > 10[/tex]
[tex]x + 2y > 8[/tex]
[tex]x,y>0[/tex]
Required
Minimum value of E
To do this, we apply graphical method
See attachment for plots of [tex]2x + y > 10[/tex] and [tex]x + 2y > 8[/tex]
From the attached plot, the point that satisfy [tex]x,y>0[/tex] is:
[tex](x,y) = (4,2)[/tex]
So, we have:
[tex]E = 1.89x + 2.89y[/tex]
This gives:
[tex]E =1.89 * 4 + 2.89 * 2[/tex]
[tex]E =7.56 + 5.78[/tex]
[tex]E =13.34[/tex]
