Answer:
The maximum value of P is [tex]40[/tex]
Step-by-step explanation:
we have the constraints
[tex]x+2y\leq 10[/tex] ------> constraint A
[tex]y\leq 2[/tex] ------> constraint B
[tex]x\geq 0[/tex] ------> constraint C
[tex]y\geq 0[/tex] ------> constraint D
[tex]P=4x+2y[/tex]
Using a graphing tool
The solution of the constraints is the shaded area in the attached figure
For the point [tex](0,0)[/tex]
The value of P is equal to
[tex]P=4(0)+2(0)=0[/tex]
For the point [tex](6,2)[/tex]
The value of P is equal to
[tex]P=4(6)+2(2)=28[/tex]
For the point [tex](0,2)[/tex]
The value of P is equal to
[tex]P=4(0)+2(2)=4[/tex]
For the point [tex](10,0)[/tex]
The value of P is equal to
[tex]P=4(10)+2(0)=40[/tex]
therefore
The maximum value of P is [tex]40[/tex]
