Question

In a cheese factory, one pie costs 3800 denars. The fixed ones costs are 1,200,000 denars, and variable costs are 2,500 denars per pie. To encounter: a) income functions. profit and costs; b) the break-even point and profit and loss intervals.

197

likes
987 views

Answer to a math question In a cheese factory, one pie costs 3800 denars. The fixed ones costs are 1,200,000 denars, and variable costs are 2,500 denars per pie. To encounter: a) income functions. profit and costs; b) the break-even point and profit and loss intervals.

Expert avatar
Eliseo
4.6
96 Answers
a) To find the income function, we can use the formula:
Income = Price per pie * Number of pies sold

In this case, the price per pie is 3800 denars. Let's denote the number of pies sold as 'x'. Therefore, the income function is:
Income = 3800x

To find the profit function, we need to subtract the total cost from the income. The total cost includes both fixed costs and variable costs. The fixed costs are 1,200,000 denars and the variable cost per pie is 2500 denars. So, the total cost function is:
Total Cost = Fixed Costs + Variable Cost per pie * Number of pies sold
Total Cost = 1,200,000 + 2500x

Now, we can find the profit function:
Profit = Income - Total Cost
Profit = 3800x - (1,200,000 + 2500x)
Simplifying this equation, we get:
Profit = 3800x - 1200000 - 2500x
Profit = 1300x - 1200000

b) The break-even point is the point where the profit is zero. To find the break-even point, we set the profit function equal to zero and solve for 'x':
1300x - 1200000 = 0
1300x = 1200000
x = 1200000/1300
x ≈ 923.08

Therefore, the break-even point is approximately 923.08 pies.

To find the profit and loss intervals, we need to analyze the profit function. If the profit is positive, it indicates a profit. If the profit is negative, it indicates a loss. If the profit is zero, it indicates the break-even point.

Let's consider two cases:
1. When x < 923.08 (before the break-even point):
Plugging in numbers less than 923.08 into the profit function, we will get a negative value. This indicates a loss.

2. When x > 923.08 (after the break-even point):
Plugging in numbers greater than 923.08 into the profit function, we will get a positive value. This indicates a profit.

Answer:
a) The income function is Income = 3800x
The profit function is Profit = 1300x - 1200000
The total cost function is Total Cost = 1,200,000 + 2500x

b) The break-even point is approximately 923.08 pies.
Before the break-even point, there is a loss.
After the break-even point, there is a profit.

Frequently asked questions (FAQs)
How many ways can 5 out of 10 people be selected for a committee?
+
What is the probability of getting a head in a fair coin toss?
+
What is the maximum value of the sine function on the interval [0, π/3]?
+
New questions in Mathematics
calculate the derivative by the limit definition: f(x) = 6x^3 + 2
10! - 8! =
8x-(5-x)
7273736363-8
1. Suppose we have a good whose quantity supplied changed from 100 to 120 units when the price increased from $10 to $12 per unit. Compute the price elasticity of supply using the midpoint method
An integer is taken at random from the first 40 positive integers. What is the probability that the integer is divisible by 5 or 6?
-0.15/32.6
Solve this mathematical problem if 3/5 of a roll of tape measures 2m. How long is the complete roll?
Emma is on a 50 m high bridge and sees two boats anchored below. From her position, boat A has a bearing of 230° and boat B has a bearing of 120°. Emma estimates the angles of depression to be about 38° for boat A and 35° for boat B. How far apart are the boats to the nearest meter?
4x + 8y = 5 2x + 4y = 10
In the telephone exchange of a certain university, calls come in at a rate of 5 every 2 minutes. Assuming a Poisson distribution, the average number of calls per second is: a) 1/8 b) 1/12 c) 1/10 d) 2/5 e) 1/24
A storage maker price is $2.50 per square feet. Find the price of a custom shed 4 yards long, and 5yards wide and 8 feet tall
P(Z<z)=0.1003
A function is considered exponential when it has a base with positive values greater than zero and different from one, where the exponent is an unknown. An important characteristic of exponential functions is that they show rapid growth or decay as an independent variable increases or decreases. Given the function 25^(x+3)=125, it is calculated that x has the value of
9 x² + 2x + 1 = 0
Show work on 4108 divided by 4
For what values of m is point P (m, 1 - 2m) in the 2⁰ quadrant?
How many cards do you expect to pull from a poker deck until you get an ACE?
Gender and communication : Answer the question ( 1 paragraph is ok) . Please can you write about women? Compared to your other identities, how much of a role does gender play in your life? And has your own sex/gender offered you privileges or disadvantages? How so?
Let I be an interval and let f : I → R be a continuous function such that f(I) ⊂ Q. Show (in symbols) that f is constant.