Math Help - [SOLVED] cost and revenue functions

1. [SOLVED] cost and revenue functions

this question has my head spinning, i can get a part of it but could use some help.

Southwest hospital has an operating room used only for eye surgery.
--the annual cost of heat, rent, and electricity for the operating room and its equipment is $180,000 and the annual salaries for the staff is$270,000
--each surgery performed requires the use of $380 worth of medical supplies and drugs. --to promote goodwill, every patient recieves a bouquet of flowers the day after the surgery. --in addition, ONE-QUARTER of the patients require dark glasses, which the hospital supplies for free. --it costs the hospital$15 for each bouquet and $20 for each pair of glasses. --the hospital recieves$1,000 for each eye operation performed.

A) find the cost function. Define your x-variable.
B) find the revenue function. r(x)=1000x ???????

as of now i have that c(x)= 380x + 180,000 + 270,000
----but do i add 15 to the 380x for the flowers, making it 395x?
----and how do i add on the glasses if they're only for 1/4 of patients?

2. Originally Posted by JGaraffa
this question has my head spinning, i can get a part of it but could use some help.

Southwest hospital has an operating room used only for eye surgery.
--the annual cost of heat, rent, and electricity for the operating room and its equipment is $180,000 and the annual salaries for the staff is$270,000
--each surgery performed requires the use of $380 worth of medical supplies and drugs. --to promote goodwill, every patient recieves a bouquet of flowers the day after the surgery. --in addition, ONE-QUARTER of the patients require dark glasses, which the hospital supplies for free. --it costs the hospital$15 for each bouquet and $20 for each pair of glasses. --the hospital recieves$1,000 for each eye operation performed.

A) find the cost function. Define your x-variable.
B) find the revenue function. r(x)=1000x ???????

as of now i have that c(x)= 380x + 180,000 + 270,000
----but do i add 15 to the 380x for the flowers, making it 395x?
----and how do i add on the glasses if they're only for 1/4 of patients?

your r(x) = 1000x is right

$c(x) = 380x + 180 000 + 270 000 + 15x + \frac{1}{4} x (20)$

$c(x) = = 380x + 180 000 + 270 000 + 15x + 5x$

$c(x) = 400x + 450 000$

3. Originally Posted by JGaraffa
this question has my head spinning, i can get a part of it but could use some help.

Southwest hospital has an operating room used only for eye surgery.
--the annual cost of heat, rent, and electricity for the operating room and its equipment is $180,000 and the annual salaries for the staff is$270,000
--each surgery performed requires the use of $380 worth of medical supplies and drugs. --to promote goodwill, every patient recieves a bouquet of flowers the day after the surgery. --in addition, ONE-QUARTER of the patients require dark glasses, which the hospital supplies for free. --it costs the hospital$15 for each bouquet and $20 for each pair of glasses. --the hospital recieves$1,000 for each eye operation performed.

A) find the cost function. Define your x-variable.
B) find the revenue function. r(x)=1000x ???????

as of now i have that c(x)= 380x + 180,000 + 270,000
----but do i add 15 to the 380x for the flowers, making it 395x?
----and how do i add on the glasses if they're only for 1/4 of patients?

$x$ = number of surgery patients

$C(x) = 180000+270000+380x+15x+\frac{x}{4} \cdot 20$
simplify by combining the like terms

yes, $R(x) = 1000x$

4. thank you for your help,

those two formulas led to the profit function being p(x) = 600x + 450,000

to find the break-even point do i just solve for x?

making the break even point 750?

5. Originally Posted by JGaraffa

those two formulas led to the profit function being p(x) = 600x + 450,000 (how?)

to find the break-even point do i just solve for x?

making the break even point 750?
Profit
P(x) = 600x - 450 000

yes, for break even, x = 450000/600 = 750

6. second question gets tweaked a little

the same statistics as my original question, however with different numbers. i think i got it down but would appreciate if someone can check it out and see if its correct.

One of the nurses has just learned of a machine that will reduce the supplies needed for each surgery by \$50 per patient. It can be leased for 50,000 annually.

a) find the new cost function if the hospital chooses to lease the machine. define the x-variable.

C(x) = 330x + 180,000 + 270,000 + 50,000 + 15x + 1/4(x(20)
C(x) = 330x + 180,000 + 270,000 + 50,000 + 15x + 5x
C(x) = 360x + 500,000

x = number of surgeries performed.

b) find the new profit function

P(x) = R(x) – C(x)
P(x) = 1000x – (360x +500,000)
P(x) = 1000x – 360x – 500,000
P(x) = 640x – 500,000

c) find the new break even point

P(x) = 640x – 500,000
500,000 = 640x
781.25 = x

d) suppose southwest averages 70 operations per month, what kind of advice would you give the administrator?

If the hospital averages 70 surgeries per month that means that 840 surgeries would be performed in one year. Based on this information more profit would be received if the machine is not leased.

P(x) = 600x – 450,000
P(x) = 600(840) – 450,000
P(x) = 504,000 – 450,000
P(x) = 54,000

P(x) = 640x – 500,000
P(x) = 640(840) – 500,000
P(x) = 537,600 – 500,000
P(x) = 37,600

thank you so much for your help.