Question

You have been hired as a consultant for Southwest Hospital to evaluate some of their business operations. The hospital board has provided the following information to help you in your evaluation:

Southwest Hospital has an operating room used only for eye surgery. The annual cost of rent, heat, and electricity for the operating room and its equipment is $341,000. The annual salaries of the people who staff this room total $559,000.

Each surgery performed requires the use of $760 worth of medical supplies and drugs. To promote goodwill, every patient receives a bouquet of flowers the day after surgery. In addition, one-quarter of the patients require dark glasses, which the hospital provides free of charge. It costs the hospital $30 for each bouquet and $40 for each pair of glasses.

The hospital receives a payment of $2,000 for each eye operation performed. The hospital currently averages 70 eye operations per month.

One of the nurses informed the board that she has recently learned about a machine that would reduce the per patient amount of medical supplies needed for each operation by $108.   The machine can be leased annually for $100,000.

An advertising agency has proposed to the hospital board that the board should spend $20,000 per month on television and radio advertising to persuade people that Southwest Hospital is the best place to have any eye surgery performed. Advertising account executives estimate that such publicity would increase business by 35 operations per month.

The board of Southwest Hospital has requested you prepare a brief report for them addressing the following:

1) Create both cost and revenue functions by identifying revenue per case and annual fixed and variable costs for running the eye surgery operating room as it currently operates (i.e. without considering the new machine or the advertising) and what is the hospital’s annual profit.

2) Based on current operations, determine how many eye operations the hospital must perform each year in order to break even with the new machine. How does this compare to current break even at Southwest Hospital (without new machine)?

Answer 1

1).

Consider the given problem here the hospital receives a payment of “$2,000” for each “eye operation”, => the “TR” function is given by, “TR = 2,000*E, where “E = number of eye operation”.

Now, the annual cost of rent, heat, and electricity for the operating room and its equipment is $341,000. The annual salaries of the people who staff this room total $559,000, => the “total fixed cost“ is given below.

=> The total fixed cost, => TFC = $341,000 + $559,000 = $900,000.

Now, each surgery performed requires the use of $760 worth of medical supplies and drugs. To promote good will, every patient receives a bouquet of flowers the day after surgery. In addition, one-quarter of the patients (E/4) require dark glasses, which the hospital provides free of charge. It costs the hospital $30 for each bouquet and $40 for each pair of glasses.

=> The total variable cost is given by, “$760*E + $30*E + $40*(E/4), => $790*E + $10*E.

=> the TVC is given by, “$800*E”.

So, the “TC” function is given by, “TC = TFC + TVC = $900,000 + $800*E.

Now the profit function is given by, “π = TR – TC = 2,000*E - $900,000 – $800*E”.

The optimum profit will be determined by the condition “MR=MC”, here “MR = 2,000” and “MC=800”.

So we can see that, “MR=2,000 > MC = 800”, here “MR” and “MC” both are constant and “MR” is more than “MC”, => addition operation always increase profit, => here the hospital will try to increase the number of operation as much as possible, because additional operation will add more revenue compared to cost.

Now, average monthly sale is “70”, => average annual sale is “70*12=840”.

So, the average annual profit is “π = TR – TC = 2,000*840 - $900,000 – $800*840”.

=> π = (2,000 – 800)*840 - $900,000 = $1,200*840 - $900,000 = $108,000 > 0.

2).

Now if we add the new machine then that would reduce the per patient amount of medical supplies needed for each operation by $108, => the variable cost will decrease by “108”, => the new variable cost is “$692*E”.

The machine can be leased annually for $100,000 and $20,000 per month on television and radio advertising, => the new fixed cost is “900,000 + 100,000 + $20,000*12 = $1,240,000.

So, the new cost function is “$1,240,000 + $692*E”. Now in order to be on the brake even the “TR” must be equal to “TC”.

=> $2,000*E = $1,240,000 + $692*E, => $1,308 =$1,240,000, => E = $1,240,000 / $1,308 = 948.

So, in order to be on the break even the sale must be “948”.

Now, without new machine the break even sale is given below.

=> 2000*E = $900,000 + $800*E, => E = 900,000/1200 = 750.

So, if we compare these two situations we can see that the break even sale is more with new machine compared to without machine. Here the total cost with machine is more compare to without machines, this is only because of the fixed cost. So, the hospital will be able to increase profit if it can able to increase its sale significantly, because “MC” has decreases under with machine case.