Chapter 4, Problem 14RP

Explanation of Solution

Goal programming model:

• Consider the following table:

	Type of operation
	1	2	3	4
Profit ($)	200	150	100	80
X-ray time (minutes)	6	5	4	3
Laboratory time (minutes)	5	4	3	2

• Suppose that
  • x₁= number of operations of type 1
  • x₂= number of operations of type 2
  • x₃= number of operations of type 3
  • x₄= number of operations of type 4
  • (s_i)^- = amount by which users are under the ith goal
  • (s_i)⁺ = amount by which users exceed the ith goal (i=1,2,3)
  • z = penalty associated with meeting the daily requirements
• A daily profit of at least $100,000 is to be earned. Therefore, we get
  • 200x₁+150x₂+100x₃+80x₄+(s₁)^-- (s₁)⁺=100000
• At most 50 hours daily of X-ray time are to be used...