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
72 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 value of (2^3)^2?
+
What is the absolute value of the product of two complex numbers: (3+4i) and (-2-5i)?
+
Math question: What is the equation of a parabola with its vertex at (4, -2) that opens upward?
+
New questions in Mathematics
Solution of the equation y&#39;&#39; - y&#39; -6y = 0
-x+3x-2,si x=3
A car tire can rotate at a frequency of 3000 revolutions per minute. Given that a typical tire radius is 0.5 m, what is the centripetal acceleration of the tire?
The sum of two numbers is 6, and the sum of their squares is 28. Find these numbers exactly
Suppose 50% of the doctors and hospital are surgeons if a sample of 576 doctors is selected what is the probability that the sample proportion of surgeons will be greater than 55% round your answer to four decimal places
A soft drink machine outputs a mean of 23 ounces per cup. The machines output is normally distributed with a standard deviation of 3 ounces. What is the probability of filling a cup between 26 and 28 ounces round your answer to four decimal places
The miles per gallon (mpg) for each of 20 medium-sized cars selected from a production line during the month of March are listed below. 23.0 21.2 23.5 23.6 20.1 24.3 25.2 26.9 24.6 22.6 26.1 23.1 25.8 24.6 24.3 24.1 24.8 22.1 22.8 24.5 (a) Find the z-scores for the largest measurement. (Round your answers to two decimal places.) z =
How many different ways can a psychology student select 5 subjects from a pool of 20 subjects and assign each one to a different experiment?
12(3+7)-5
The average number of babies born at a hospital is 6 per hour. What is the probability that three babies are born during a particular 1 hour period?
3. A rock is dropped from a height of 16 ft. It is determined that its height (in feet) above ground t seconds later (for 0≤t≤3) is given by s(t)=-2t2 + 16. Find the average velocity of the rock over [0.2,0.21] time interval.
Determine the reduced form of the slope equation equal to 2
Two minus log 3X equals log (X over 12)
3%2B2
Congratulations, you have saved well and are ready to begin your retirement. If you have $1,750,000.00 saved for your retirement and want it to last for 40 years, and will earn 10.8% compounded monthly: What is the amount of the monthly distribuion? 216.50 How much interest is earned in retirement?
Jasminder has made 55% of the recipes in a particular cookbook. If there are 9 recipes that he has never made, how many recipes does the cookbook contain?
A natural gas company has a fixed rate of 1,320 pesos plus 1,590 pesos per cubic meter of gas consumed monthly per customer. Indicate the cost function to determine the value in pesos of the cubic meters of gas consumed in a month per customer. How much did a customer who consumed 18 cubic meters of gas pay? If a customer paid 34,710 pesos, how many cubic meters of gas did he consume?
Find the vertex F(x)=x^2-10x
Farm Grown, Inc., produces cases of perishable food products. Each case contains an assortment of vegetables and other farm products. Each case costs $5 and sells for $15. If there are any not sold by the end of the day, they are sold to a large food processing company for $3 a case. The probability that daily demand will be 100 cases is 0.30, the probability that daily demand will be 200 cases is 0.40, and the probability that daily demand will be 300 cases is 0.30. Farm Grown has a policy of always satisfying customer demands. If its own supply of cases is less than the demand, it buys the necessary vegetables from a competitor. The estimated cost of doing this is $16 per case. (a) Draw a decision table for this problem (b) What do you recommend?
x²-7x+12=0