a paper manufacturing company recycles paper, cans and other sheet metal. the profit on the paper is $500 and the profit on the cans is $350 per pound
A) write the objective function that models the daily profit
B) the manufacture is bound by the following constraints , namely:
*equipment allows at most 200lbs of can a day at the same time
*equipment allows at most 200lbs of paper per day
*equipment require at least 10kbs of paper and 80lbs of cans to operate
*equipment allows for recycling at msot 300bs of cans per day
C) graph the inequalities from equations in B
D)evaluate the objective function at each of the vertices and determine the mix of cans and paper for max profit
Are you sure? The company gets $350 per pound for cans??????
A) The objective function that models the daily profit can be defined as follows:
Let x be the number of pounds of paper recycled per day, and y be the number of pounds of cans recycled per day. The daily profit (P) can be calculated as:
P = 500x + 350y
B) Now, let's formulate the constraints based on the given information:
1) The equipment allows at most 200 pounds of cans per day:
y ≤ 200
2) The equipment allows at most 200 pounds of paper per day:
x ≤ 200
3) The equipment requires at least 10 pounds of paper and 80 pounds of cans to operate:
x ≥ 10
y ≥ 80
4) The equipment allows for recycling at most 300 pounds of cans per day:
y ≤ 300
C) To graph the inequalities from the equations in B, you can plot each constraint on a coordinate system. The x-axis represents the pounds of paper (x) and the y-axis represents the pounds of cans (y). The lines representing the constraints are as follows:
1) y ≤ 200: This is a horizontal line at y = 200.
2) x ≤ 200: This is a vertical line at x = 200.
3) x ≥ 10: This is a vertical line at x = 10.
4) y ≥ 80: This is a horizontal line at y = 80.
5) y ≤ 300: This is a horizontal line at y = 300.
D) To evaluate the objective function at each of the vertices, we need to find the intersection points of the lines representing the constraints. The vertices are the points where the lines intersect. Once we have the coordinates of the vertices, we substitute the values into the objective function to find the profit at each vertex. The mix of cans and paper for maximum profit will be determined by comparing the profit values at each vertex.
Note: The process to find the vertices and evaluate the objective function at each vertex can be done using graphical methods or linear programming techniques such as the Simplex algorithm.