Homework Help

If the area shaded in Part A above represents the solution set to a linear programming...

user profile pic

davene25 | Student, Undergraduate | (Level 1) eNoter

Posted September 12, 2013 at 3:17 PM via web

dislike 0 like

If the area shaded in Part A above represents the solution set to a linear programming problem.  Show which combination within the set would maximize the objective function P = 10x + 8y, where P represent profit, and X and Yare the amount of good X and good Y respectively which the firm sells.

Images:
This image has been Flagged as inappropriate Click to unflag
Image (1 of 1)

1 Answer | Add Yours

user profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted September 12, 2013 at 3:36 PM (Answer #1)

dislike 0 like

The area shown has four boundaries. One of them is the line y/10 + x/5 = 1 => y = -2x + 1. The slope of this line is -2.

With each increment in x, the value of y decreases by 2.

The maximum value of P = 10x + 8y is at the point in the area where the value of x is maximum, this is (8, 1).

The value of P is maximum at (8, 1)

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes