cAnything helps and if i could get an explanation cause im a bit lost!
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!
1a. The fixed costs (FC) for running the operating room are $450,000 (rent, heat, and electricity) and the variable costs (VC) are $370x (medical supplies and drugs), where x is the number of patients.
b. The cost function is C(x) = FC + VC = $450,000 + $370x.
2. The revenue function is R(x) = $1000x, where x is the number of eye operations performed.
3. To break even, the total cost should equal the total revenue. So we have C(x) = R(x), which means $450,000 + $370x = $1000x. Solving this equation, we find x = 750. Therefore, the hospital must perform 750 eye operations per year to break even.
4. With the medical machine that reduces medical supplies costs by $50 per patient, the new variable cost would be $370 - $50 = $320 per patient. The new cost function would be C(x) = $450,000 + $320x. To determine if leasing the machine is justified, we need to compare the costs with and without the machine.
With the machine:
C(x) = $450,000 + $320x
Without the machine:
C(x) = $450,000 + $370x
We can compare the costs when the number of eye operations is 840:
C(840) = $450,000 + $320(840) = $450,000 + $268,800 = $718,800
C(840) = $450,000 + $370(840) = $450,000 + $310,800 = $760,800
The total cost with the machine is $718,800, while the total cost without the machine is $760,800. Since the cost is lower with the machine, it is justified to lease it.
5. The revenue from the additional 480 operations due to advertising would be R(x) = $1000(480) = $480,000. However, we need to subtract the cost of advertising, which is $120,000. So the impact on profits would be $480,000 - $120,000 = $360,000.
6. To cover the cost of the proposed ads ($120,000), the hospital needs to bring in additional revenue. Since each operation brings in $1000, the number of extra patients needed is $120,000 / $1000 = 120.
7. If the ad campaign meets its projections and brings in an additional 480 operations per year, the hospital's revenue will increase by $1000(480) = $480,000. However, we need to consider both the increased revenue and the cost of leasing the machine.
Total revenue: $480,000
Total cost with the machine: $450,000 + $320(840) = $718,800
With the increased revenue, the total profit would be $480,000 - $718,800 = -$238,800 (negative profit). Therefore, the hospital should not purchase the machine in this scenario, as it would result in a loss.
1a. To identify the annual fixed and variable costs for running the operating room, we need to understand which costs remain constant regardless of the number of surgeries performed (fixed costs) and which costs vary depending on the number of surgeries (variable costs).
Fixed Costs (FC): These costs do not change with the number of surgeries performed. In this scenario, 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. Therefore, the fixed costs would be $200,000 + $250,000 = $450,000.
Variable Costs (VC): These costs vary depending on the number of surgeries performed. For each surgery, the cost of medical supplies and drugs is $370. Additionally, every patient receives a $25 bouquet of flowers, and one-quarter of the patients receive a $20 pair of dark glasses. Therefore, the variable costs per surgery would be $370 + $25 + ($20/4) = $370 + $25 + $5 = $400.
b. The cost as a function of the number of patients having eye surgery in a year, denoted by x, can be written as:
C(x) = FC + (VC * x)
= $450,000 + ($400 * x)
2. The revenue function can be written as:
R(x) = $1,000 * x
3. To break even, the hospital's total revenue should be equal to its total cost.
So, equating the cost function C(x) to the revenue function R(x), we get:
C(x) = R(x)
$450,000 + ($400 * x) = $1,000 * x
Solving the above equation, we find:
$450,000 = $1,000 * x - ($400 * x)
$450,000 = $600 * x
x = $450,000 / $600
x = 750
Therefore, the hospital must perform 750 eye operations each year to break even.
4. Currently, the hospital averages 840 eye operations per year. If a medical machine can reduce the cost of medical supplies by $50 per patient, we need to determine if the savings from the machine lease outweigh the cost of the lease.
Savings per year due to the machine = $50 * 840 = $42,000
Since the cost of leasing the machine is $50,000 annually, and the savings are less than the lease cost, it would not be financially beneficial for the hospital to lease the machine in this case.
5. If the advertising agency spends $120,000 per year on advertising and it is estimated that it will increase business by 480 operations per year, we need to calculate the impact on the hospital's profits.
Increased revenue due to advertising = $1,000 * 480 = $480,000
The cost of advertising is $120,000 per year. Therefore, the impact on the hospital's profits would be:
Impact on profits = Increased revenue - Cost of advertising
= $480,000 - $120,000
= $360,000
The advertising would increase the hospital's profits by $360,000.
6. To determine the number of extra patients per year needed to cover the cost of the proposed ads, we need to calculate how many patients would be required to generate $120,000 in revenue.
Revenue per patient = $1,000
Number of patients needed = Cost of advertising / Revenue per patient
= $120,000 / $1,000
= 120
Therefore, the hospital would need 120 additional patients per year to cover the cost of the proposed ads.
7. If the ad campaign is approved and subsequently meets its projections, the hospital would have an additional revenue of $480,000 per year. Considering the savings generated from reduced medical supplies, the scenario will change.
Savings per year due to the machine = $50 * 840 = $42,000
Additional revenue + Savings - Cost of leasing machine = $480,000 + $42,000 - $50,000 = $472,000
The hospital would have an increased profit of $472,000 if the ad campaign meets its projections. Given this increased profit, it would make sense for the hospital to purchase the machine. The combined impact of increased revenue and savings would outweigh the cost of leasing the machine, resulting in higher overall profitability for the hospital.
1a. To identify the fixed costs (FC) and variable costs (VC) for running the operating room, we need to determine which costs remain constant regardless of the number of surgeries (fixed costs) and which costs vary based on the number of surgeries (variable costs).
In this case:
Fixed costs (FC) include the annual cost of rent, heat, and electricity for the operating room and its equipment, as well as the annual salaries for the people who staff the room. So FC = $200,000 + $250,000 = $450,000.
Variable costs (VC) include the cost of medical supplies and drugs used for each surgery, the cost of bouquets of flowers, and the cost of dark glasses for a quarter of the patients. VC = $370 + $25 + (1/4) * $20 = $370 + $25 + $5 = $400.
b. Since the fixed cost is $450,000 and the variable cost is $400 per surgery, we can write the cost (C) as a function of the number of patients (x) having eye surgery in a year:
C(x) = FC + VC(x)
= $450,000 + $400x
2. The revenue function can be written as the payment received for each eye operation performed (which is $1000) multiplied by the number of surgeries (x):
R(x) = $1000x
3. To break even, the hospital's cost (C) and revenue (R) should be equal. Therefore, we can set C(x) = R(x) and solve for x:
$450,000 + $400x = $1000x
$600x = $450,000
x ≈ 750 surgeries
So, the hospital must perform 750 eye operations each year to break even.
4. To decide whether the hospital should lease the medical machine, we need to compare the cost savings from reduced medical supplies with the cost of leasing the machine.
Given that the machine reduces the amount of medical supplies needed by $50 per patient and there are 840 eye operations per year, the total cost savings would be $50 * 840 = $42,000.
Since the cost of leasing the machine is $50,000 annually, if the cost savings from reduced medical supplies are less than $50,000, it would not be cost-effective to lease the machine. In this case, the cost savings of $42,000 are less than the leasing cost of $50,000, so it would not be justified to lease the machine.
5. If the hospital spends $120,000 per year on advertising and this results in an increased business of 480 eye operations per year, we can calculate the additional revenue generated.
The additional revenue can be calculated by multiplying the increased operations (480) by the payment received for each eye operation ($1000):
Additional revenue = 480 * $1000 = $480,000
To determine the impact on the hospital's profits, we need to subtract the cost of advertising from the additional revenue:
Impact on profits = Additional revenue - Advertising cost
= $480,000 - $120,000
= $360,000
So, the advertising would have an impact of $360,000 on the hospital's profits.
6. To determine how many extra patients per year are needed to cover the cost of the proposed ads, we divide the advertising cost ($120,000) by the revenue per surgery ($1000):
Extra patients = Advertising cost / Revenue per surgery
= $120,000 / $1000
= 120 patients
Therefore, the hospital would need 120 extra patients per year to cover the cost of the proposed ads.
7. If the ad campaign is approved and meets its projections resulting in 480 additional eye operations per year, we need to assess whether the increased revenue justifies leasing the medical machine.
At this point, the hospital would have a total of 840 + 480 = 1,320 eye operations per year.
To determine the cost savings from reduced medical supplies, we multiply the reduced amount per patient ($50) by the number of surgeries (1,320):
Cost savings = $50 * 1,320 = $66,000
Since the cost savings of $66,000 are higher than the cost of leasing the machine ($50,000), it would be justified for the hospital to purchase the machine.
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.