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A local surgical clinic specializes in two types of surgeries for their authorized patients. Summarizing the difficulties of insurance, payment, and elective surgery demand we have the following knowledge: type A surgeries provide a net benefit of $900 per surgery to the clinic and type B provide $1200. Of course, there are constraints as well. Type A surgeries generally require 2 hours of surgery time and 2 hours of patient physical therapy/follow-up post surgery. Type B surgeries require 4 hours of surgery time and 8 hours of physical therapy/follow-up per week. There are only 80 person-hours available for surgery and 110 person-hours available for therapy and follow-up. a.) Write this question as a linear programming problem. b.) Determine the quantity of each type of surgery that will optimize the clinic’s profit. c.) Find the shadow price on surgery hours available AND interpret this shadow price (i.e. explain to someone who has no idea what a shadow price is what the shadow price means.)
Expert Answer
a)
Let the number of Type A surgeries be denoted by A & number of type B surgeries be denoted by B
Objective function:
Maximize: 900*A + 1200*B
Subject to:
2*A + 4*B <= 80
2*A + 8*B <= 110
b)
Solving using Excel Solver the answer is as below:
Optimized numbers:
A = 40
B = 0
Optimized profit = 36000
c) The shadow price is 450
This implies that for every unit increase in the constraint i.e. increase in number of hours available for surgery by 1, the profit increases by $450.
