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
107 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)
Question: Find the absolute extrema of f(x) = x^3 - 3x^2 + 2x on the interval [-1, 3].
+
What is the slope of a line passing through the points (-2, 4) and (3, 10)?
+
What is the length of the hypotenuse of a right triangle with legs measuring 4 cm and 8 cm?
+
New questions in Mathematics
A=m/2-t isolate t
Using a remarkable product you must factor the expression: f(x) =36x^2-324 and you are entitled to 5 steps
3(2+x)-2(2x+6)=20-4x
How many percent is one second out a 24 hour?
what is 3% of 105?
5) A family with a father, mother and 3 children must sit on five chairs in a row and the only restriction is that the mother must be at one end. In how many different ways can they be seated?
58+861-87
Two numbers differ by 7, and the sum of their squares is 29. Find the numbers.
A bird randomly chooses to land on 1 of 12 perches available in its aviary. Determine the Probability of it landing on a perch numbered 8 and then on a perch marked with a prime number; take into account that he never lands on the same perch in the sequence.
By direct proof, how can you prove that “The sum of any three consecutive even integers is always a multiple of 6”.
A recurring sequence is one where elements repeat after completing one standard. If the sequence AB8C14D96AB8C1... is recurring its twentieth term is equal to: (A) B. (B) 8. (C) A. (D) 6. (E) D.
From 1975 through 2020 the mean annual gain of the Dow Jones Industrial Average was 652. A random sample of 34 years is selected from this population. What is the probability that the mean gain for the sample was between 400 and 800? Assume the standard deviation is 1539
Determine the increase of the function y=4x−5 when the argument changes from x1=2 to x2=3
The two sides of the triangle are 12 cm and 5 cm, and the angle between the sides is 60°. Cover the area of ​​the triangle!
392929-9
Sabendo+que+o+tri%C3%A2ngulo+ABC+%C3%A9+ret%C3%A2ngulo+e+que+um+de+seus+%C3%A2ngulos+mede+30+quanto+mede+o+terceiro+ tri%C3%A2ngulo
We have received our p&l statement back from accounts. The board has asked for an innovation hub. What items should we prioritise reviewing to decide if we can afford an innovation hub?
4m - 3t + 7 = 16
Solve the system of equations by the addition method. 0.01x-0.08y=-0.1 0.2x+0.6y=0.2
(3b)⋅(5b^2)⋅(6b^3)