Solution
- In order to find the minimum value of P, we need to substitute the values of x and y from the boundaries of the shaded region.
- The coordinates of the shaded region are highlighted below:
- The smallest value we get from substituting these values of x and y will be the minimum value of P.
- Thus, we have:
[tex]\begin{gathered} P=12x+15y \\ \\ \text{ When }(0,7)\text{ is used:} \\ P=12(0)+15(7) \\ P=105 \\ \\ \text{ When }(1,7)\text{ is used:} \\ P=12(1)+15(7) \\ P=117 \\ \\ \text{ When }(0,4)\text{ is used:} \\ P=12(0)+15(4) \\ P=60 \\ \\ \\ \text{ When }(3,1)\text{ is used:} \\ P=12(3)+15(1) \\ P=51 \end{gathered}[/tex]
Final Answer
The minimum value of P is 51
