cAnything helps and if i could get an explanation cause im a bit lost!

Question

thank youuuu (:

A 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 $200,000 and the annual salaries for the people who staff this room total $250,000.

Each surgery performed requires the use of $370 worth of medical supplies and drugs. Every patient receives a $25 bouquet of flowers the day after surgery. Also, one-quarter of the patients receive a $20 pair of dark glasses.

1a. Identify the annual fixed and variable costs for running the operating room.
FC=?
VC=?
b. Let x be the number of patients having eye surgery in a year. Write the cost as a function of x
C(x)=(this is what i think it is)===450,000+400x

2.The hospital receives a payment of $1000 for each eye operation performed. Write the revenue function.
R(x)= (this is what i think it is)===1000x

3. How many eye operations must the hospital perform each year in order to break even?
=====For this one i think you set them equal to each other and solve for x which is 750 surgeries correct?

4. currently the hospital averages 840 eye operations per year. There is a medical machine that would reduce by $50 per patient the amount of medical supplies needed Should the hospital lease this machine if it can be leased for $50,000 annually. Justify your answer.

5. Ad advertising agency has proposed to the hospital's president that she spend $120,000 per year on television and radio advertising to persuade people that Southwest Allentown Hospital is the best place to have an eye surgery performed. Adversiting account executives estimate that such publicity would increase business by 480 opertions per year. What impact would this adversiting have on the hospital's profits?

6. In case the advertising agency is being overly optimistic, how many extra patients per year are needed to cover the cost of the proposed ads? Justify your answer.

7.If the ad campaign is approved and subsequently meets its projections, should the hospital purchase the machine mentioned earlier? Justify your answer!

Answer 1

1a. FC = 200,000 + 250,000 = $450,000.

VC = (370 + 25)x + 20x / 4,
VC = 395x + 5x = 400x.

Your answers are correct, but you should show your work.

b. C(x) = 400x + 450,000.

2. Correct!

3. Correct! Very good!

4. Net Savings = $50*840 - $50000 = -$8,000. = $8000 Loss. They should not lease.

5. Net Increase=$1000*480 - $120,000 = $360,000.

6. 1000x = 120,000, X = 120 extra Patients.

7. Net Savings = 50(840+480) - 50000 = $16,000 / yr. That's small when compared with the increase received from advertising. They shouldn't buy the machine.