help with filling out the boxes based on the passage in regard to optimization

Scenario: You are in charge of surgery services of the Hospital. It specializes in two kinds Lot of Mercy Hospital of surgeries: heart surgery and nose surgery. As per the internal reports form the accounts division, each heart surgery brings in a profit of $8750; and each nose surgery makes profit of $2450. You are located in downtown Atlanta and there is a lot of demand for both surgeries. However, the Hospital has limited capacity and resources (i.e., rooms, doctors and nurses etc.) available for surgeries. Your office has to decide how many of each type of surgery to be offered every month. completed, while the nose surgery only two hours. Each heart surgery requires two doctors, that is, 12 doctor hours to be accomplished, whereas the nose procedure requires only one, that is, two doctor hours. Moreover, the heart surgery requires the help of three nurses, that is, 18 nurse hours, while the nose surgery requires the help of only two, that is, 4 nurse hours. For the following month you estimate you will have available a total of 144 hours of uptime of the surgery room. Also, you count that you can use up to 240 doctor hours, and 400 nurse hours. How many heart surgeries would you approve? How many nose surgeries? Your predecessor, who if I might add, did not take MGS 4140(just bragging!) used to give priority to more profit making items or sometimes used a first-come-first-serve type rule to approve surgeries that were performed. Before coming to Lot-of-Mercy, you worked for Lot-of-Sense Hospital. When you looked at the numbers (profits) at Mercy and you started to compare them with your memory of the numbers from your previous work, you started to get a feeling that you can improve the surgery profits at Mercy. So you started to dig a little deeper. You found that, besides the number of doctors and their hours, and nurses and their hours, and the only surgery room the hospital has, you have all that is necessary to carry on with any number of surgeries. Do a back-of-the-envelope analysis and try to answer the question: How many heart and nose surgeries should you plan for next month if you want to maximize your profits? How to think about optimization ... let's mull over this problem ... one way to go about this is to find out if you do only most profit making surgery what happens? Heart surgery makes way more profit than nose. If you offer heart surgeries as much as possible, that will be 12 doctor hours per surgery and 240 hrs available - so, 240/12=20 heart surgeries. This will max out on doctors time and will take 20*18 - 360 nurse hrs; 20*6=120 room hrs - both are less than what is available; so it is doable. But no doctors left for nose surgery; but bey, maybe it will max profit , which will be 20*88750 = $175,000. On the other hand, what will be your profit if you allowed as many nose surgeries as possible? Please find this number on your own and then check with mine. If my number is correct, you can do a max 72 nose surgeries, with a profit of 72*$2450 = $176,400. What? The total profit is more than doing more profit making heart surgery. your predecessor But, is this the best profit? What and how many surgeries should you upprove? 34 won't like it!) Exercise 3 Objective: This exercise is written to help you take your familiarity and understanding of one problem to another new problem. The familiar problem: Surgery optimization at Lot-of-Mercy Hospital The new problem: Please fill up the information. Familiar Problem: New Problem: Lot-of-Mercy Surgery Optimization Problem What you trying to optimize (i.e., Maximize or Minimize)? (That is what is your objective) What you are trying to decide? (That is, what are your decision variables?) How much each of these variables contributes to your objective? How much resources each variables consume or take up? What is stopping you from offering infinite (read: a huge) number of both surgeries so that you can make a killing? Is there any special requirements that you decision has to satisfy? (For example, you have to offer at least 20 nose surgeries due to an agreement with county government ...)