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
108 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)
Math Question: What is the integral of x^n with respect to x, where n is a constant
+
Find the value of sinh(cos^-1(4/5)) + cosh(tan^-1(-3/4)), where sinh(x) represents the hyperbolic sine function and cosh(x) denotes the hyperbolic cosine function.
+
Math question: If two triangles have two sides that are equal in length and the included angles are also equal, does that guarantee that the triangles are congruent?
+
New questions in Mathematics
I want to divide R$ 2200.00 between Antônio, Beto and Cássia, so that Beto receives half from Antônio and Cássia receives a third of Beto. Under these conditions, how much more will Beto receive than Cássia?
the value of sin 178°58&#39;
A car that starts from rest moves for 11 min, reaching a speed of 135 km/h, calculate the acceleration it had
3x+5y=11 2x-3y=1
The ratio of tomatoes to red apples is 2:5. If there are 20 tomaoes in the garden, how many red apples are there?
v Is the following statement a biconditional? If Shannon is watching a Tigers game, then it is on television.
2x+4x=
Nice's central library building is considered one of the most original in the world, as it is a mix between a sculpture and a work of habitable architecture. It was called La Tête Carrée and is made up of part of a bust that supports a cube divided into five floors. It is known that the building has a total height of approximately 30 meters. It admits that the cubic part of the sculpture is parallel to the floor and has a volume of 2744 meters3 Calculate, in meters, the height of the bust that supports the cube. Displays all the calculations you made.
89, ÷ 10
Use a pattern to prove that (-2)-(-3)=1
Find the center coordinates and radius of a circle for an equation written as: 3x2 + 3y2 - 6y = —12× + 24
Professor Vélez has withdrawn 40 monthly payments of $3,275 from her investment account. If the investment account yields 4% convertible monthly, how much did you have in your investment account one month before making the first withdrawal? (Since you started making withdrawals you have not made any deposits.)
ind the z-score for which 72% of the distribution's area lies between -z and z. -1.7417, 1.7417 -1.1538, 1.1538 -1.0803, 1.0803 -2.826, 2.826
Take the limit of (sin(x-4))/(tan(x^2 - 16) as x approaches 4.
The business college computing center wants to determine the proportion of business students who have personal computers (PC's) at home. If the proportion is greater than 35%, then the lab will modify a proposed enlargement of its facilities. Suppose a hypothesis test is conducted and the test statistic is z= 2.6. Find the P-value for this test.
If the mean of the following numbers is 17, find the c value. Produce an algebraic solution. Guess and check is unacceptable. 12, 18, 21, c, 13
calculate the product of 4 and 1/8
Solve the system of equations by the addition method. 0.01x-0.08y=-0.1 0.2x+0.6y=0.2
Suppose a car license plate consists of 2 letters and two digits of which the first cannot be zero. How many different plates can be engraved? consider only 26 letters and 10 digits draw an example of this.
A plant found at the bottom of a lake doubles in size every 10 days. Yeah It is known that in 300 days it has covered the entire lake, indicate how many days it will take to cover the entire lake four similar plants.