∵ Since they will make 4 pants and 2 jackets
∵ The profit of a pair of pants is $3
∵ The profit of a jacket is $7
∴ P = 3x + 7y
We will take the vertices of the shaded area and substitute them in the equation above to find the maximum profit.
∵ The vertices are (4, 7), (4, 2), (11, 2), (10, 4)
∵ x = 4 and y = 7
[tex]\begin{gathered} \therefore P=3(4)+7(7) \\ \therefore P=12+49 \\ \therefore P=61 \end{gathered}[/tex]∵ x = 4 and y = 2
[tex]\begin{gathered} \therefore P=3(4)+7(2) \\ \therefore P=12+14 \\ \therefore P=26 \end{gathered}[/tex]∵ x = 11 and y = 2
[tex]\begin{gathered} \therefore P=3(11)+7(2) \\ \therefore P=33+14 \\ \therefore P=47 \end{gathered}[/tex]∵ x = 10 and y = 4
[tex]\begin{gathered} \therefore P=3(10)+7(4) \\ \therefore P=30+28 \\ \therefore P=58 \end{gathered}[/tex]The maximum value is $61
∴ The maximum profit is $61
∴ The amounts for the maximum profit are 4 pair of pants and 7 jackets
