Question

What is the maximum value of the objective function, P, with the given constraints?

Answer 1

Answer:

C. 450

Step-by-step explanation:

Plot the solution area for the system of four inequalities

$\left\{\begin{array}{l}4x+y\le 16\\x+y\le 10\\x\ge 0\\y\ge 0\end{array}\right.$

You'll get the quadrilateral with vertices at points (0,0), (0,10), (2,8) and (4,0).

The maximum value of the function can be at vertices, so

$P=25x+45y\\ \\P(0,0)=25\cdot0+45\cdot 0\\ \\P(0,10)=25\cdot 0+45\cdot 10=450\\ \\P(2,8)=25\cdot 2+45\cdot 8=50+360=410\\ \\P(4,0)=25\cdot 4+45\cdot 0=100$

The maximum value of the function is 450 at point (0,10)