10.4 A hospital is evaluating the feasibility of offerings among three technolog
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Question
10.4 A hospital is evaluating the feasibility of offerings among three technologies, on the basis of what would make the most profit. These new technologies are: 1. Closed-chest cardiac bypass surgery with ?daVinci Surgical Robot? 2. Gamma knife 3. Positron emission tomography (PET) scanner Table EX 10.4 gives the information on profit, the amount of common resources used by each of the three technologies per case, and their available resources per month: a. Formulate this as a linear programming problem. b. Solve the problem using Excel solver. c. Based on optimal solution, which product(s) should be offered, and how many procedures can be offered in a month? d. What is the expected contribution of new technology to the hospital?s monthly profits?Explanation / Answer
a. let the number of cases handled by daVinci, Gamma and PET be "D", "G", "P" respectively
profit = 2000D+3500G+2000P
This is the objective function and we have to maximize it.
The constraints are:
1. total staff time is 2000 hours. 15D+12G+1.5P<=2000
2. maintenance time is 1500 minutes. 25D+25G+22P<=1500
3. computer resources time is 3000 minutes. 20D+25G+10P<=3000
4. D,G,P>=0
b.
The model using the above constraints and objective function is build on excel and solved using solver to give the following solution:
c.
Based on the optimal solution, only Gamma knife should be offered. 60 procedures can be offered in a month.
d. Monthly profit = no. of cases*profit per case = 60*3500 = $210,000
No of cases solved by: Davinci Gamma PET 0 60 -1.6E-15 Profit per case Davinci Gamma PET 2000 3500 2000 Total profit per technology Total Davinci Gamma PET 0 210000 -3.3E-12 210000 This is the objective function Constraints 1. Total staff time Davinci Gamma PET Total per case 15 12 1.5 total 0 720 -2.5E-15 720 <=2000 2. Maintenance Davinci Gamma PET Total per case 25 25 22 total 0 1500 -3.6E-14 1500 <=1500 3. Computer resources Davinci Gamma PET Total per case 20 25 10 total 0 1500 -1.6E-14 1500 <=3000Related Questions
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