Question

Solve the following maximization problem graphically.

Answer 1

The maximized value of the function is (c) 119/2

Maximization problem

Maximization problems are used to determine the optimal solution of a linear programming model

Objective function

The objective function is given as:

$P(x,y) = 11x + 10y$

Constraints

The constraints are given as:

$22x + 2y \le 68$

$8x + 16y \le 68$

$x,y\ge 0$

Graph

See attachment for the graph of the constraints

From the graph, the optimal solution is: (2.83, 2.83)

So, the maximized value is:

$P(x,y) = 11x + 10y$

$P =11 \times 2.833 + 10 \times 2.833$

$P =59.493$

Approximate

$P =59.5$

Rewrite as a fraction

$P =\frac{119}{2}$

Hence, the maximized value of the function is (c) 119/2

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