Maximize

P=60x+50y

x+y≤80
5x+10y≤560
50x+20y≤1600
x≥0
y≥0


s =

the intersection with p max is of

5x+10y=560 and 50x+20y=1600

x = 12, y=50 and p = 3220
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To maximize the function P=60x+50y given the constraints, we can use the method of linear programming.

First, plot the feasible region by graphing the inequalities.

1. x+y≤80: This inequality represents the line x+y=80. Plot the line and shade the region below it.
2. 5x+10y≤560: Divide both sides of the inequality by 10 to obtain x+2y≤56. This represents the line x+2y=56. Plot the line and shade the region below it.
3. 50x+20y≤1600: Divide both sides of the inequality by 20 to obtain 5x+2y≤80. This represents the line 5x+2y=80. Plot the line and shade the region below it.
4. x≥0: This inequality represents the vertical line x=0. Plot the line and shade the region to the right of it.
5. y≥0: This inequality represents the horizontal line y=0. Plot the line and shade the region above it.

The feasible region is the overlapping shaded region that satisfies all the constraints.

Next, identify the corner points of the feasible region. These are the points where the lines intersect.

Once you have the corner points, evaluate the objective function P=60x+50y at each corner point. The corner point that gives the highest value of P will be the solution.

Therefore, to maximize P=60x+50y, calculate the value of P at each corner point and choose the maximum value as the solution.