Question 4.63

33. A linear-programming problem has constraints given by , , , and .

  1. Which, if any, of the constraints involve vertical and horizontal lines?
  2. Sketch a graph of the feasible region.
  3. What are the corner points of the feasible region?
  4. If profit is given by the expression :
    1. What is the profit associated with the point (3, 1)?
    2. Which corner points have higher profit than (3, 1)?

33.

(a) and are vertical constraints, while y=0 is a horizontal constraint.

(b)

image

(c) (0, 0); (4, 0); (4, 2); (0, 15)

(d) (i) 16; (ii) (0, 15); (4, 2)