Answer:
The maximum value of p is 18
Step-by-step explanation:
we have
[tex]5x+y \leq16[/tex] ------> constraint A
[tex]2x+3y \leq22[/tex] ----> constraint B
[tex]x\geq 0[/tex] ----> constraint C
[tex]y\geq 0[/tex] ----> constraint D
using a graphing tool
The solution is the shaded area
see the attached figure
The vertices of the solution area are
(0,0), (0,7.3), (2,6) and (3.2,0)
To find the maximum value of p, substitute the value of x and the value of y of each vertices in the equation and then compare the results
[tex]p=3x+2y[/tex]
For (0,0)
[tex]p=3(0)+2(0)=0[/tex]
For (0,7.3)
[tex]p=3(0)+2(7.3)=14.6[/tex]
For (2,6)
[tex]p=3(2)+2(6)=18[/tex]
For (3.2,0)
[tex]p=3(3.2)+2(0)=9.6[/tex]
therefore
The maximum value of p is 18
