MathMaster logo

MathMaster

  1. Home
  2. general
  3. duocuc 2 the cost c in pesos for the production of x meters of a certain fabric can be calculated through the function x 1
Question

DuocUC 2) The cost C, in pesos, for the production of x meters of a certain fabric can be calculated through the function: (x+185) C(x)=81300-6x+ 20000 a) It is known that C(90) 5.344. Interpret this result. (2 points) b) Calculate C'(x) (2 points) 3 x²+111x-0.87 20000 2000 c) Function C calculates the cost while producing a maximum of 500 meters of fabric. Determine the values of x at which the cost of production is increasing and the values of x at which the cost is decreasing. (3 points) d) If a maximum of 500 meters of fabric are produced, what is the minimum production cost? (

189

likes
945 views

Answer to a math question DuocUC 2) The cost C, in pesos, for the production of x meters of a certain fabric can be calculated through the function: (x+185) C(x)=81300-6x+ 20000 a) It is known that C(90) 5.344. Interpret this result. (2 points) b) Calculate C'(x) (2 points) 3 x²+111x-0.87 20000 2000 c) Function C calculates the cost while producing a maximum of 500 meters of fabric. Determine the values of x at which the cost of production is increasing and the values of x at which the cost is decreasing. (3 points) d) If a maximum of 500 meters of fabric are produced, what is the minimum production cost? (

Expert avatar
Jett
4.7
97 Answers
a) To interpret the result C(90) = 5,344, we substitute x=90 into the equation C(x) = 81300 - 6x + 20000:

C(90) = 81300 - 6(90) + 20000
= 81300 - 540 + 20000
= 81800 - 540
= 81260

The result C(90) = 5,344 means that the cost for producing 90 meters of fabric is 5,344 pesos.

Answer: The cost for producing 90 meters of fabric is 5,344 pesos.

b) To calculate C'(x), we differentiate the function C(x) = 81300 - 6x + 20000 with respect to x:

C'(x) = -6

Answer: C'(x) = -6

c) To determine the values of x at which the cost of production is increasing or decreasing for C(x) with a maximum of 500 meters of fabric, we need to analyze the sign of C'(x).

Since C'(x) is constant and equal to -6, it is always negative. Therefore, the cost of production is always decreasing for C(x) with a maximum of 500 meters of fabric.

Answer: The cost of production is always decreasing for C(x) with a maximum of 500 meters of fabric.

d) To find the minimum production cost when a maximum of 500 meters of fabric is produced, we substitute x=500 into the equation C(x) = 81300 - 6x + 20000:

C(500) = 81300 - 6(500) + 20000
= 81300 - 3000 + 20000
= 98300 - 3000
= 95300

The minimum production cost when a maximum of 500 meters of fabric is produced is 95,300 pesos.

Answer: The minimum production cost when a maximum of 500 meters of fabric is produced is 95,300 pesos.

Frequently asked questions (FAQs)
Question: "What are the solutions of the quadratic equation 2x^2 + 5x + 3 = 0?"
+
Math question: Find the absolute extrema of the function f(x) = x^2 - 4x + 5 on the interval [-2, 5].
+
What is the domain of the square root function f(x) = √(x-3)?
+
New questions in Mathematics
Add. 7/w²+18w+81 + 1/w²-81
12-6x=4x+2
What is the amount of interest of 75,000 at 3.45% per year, at the end of 12 years and 6 months?
a) A tap can supply eight gallons of gasoline daily to each of its 250 customers for 60 days. By how many gallons should each customer's daily supply be reduced so that it can supply 50 more customers for twenty more days?
The length and breadth of my rectangular vegetable garden is 12,5m and 7,25m respectively. What is the perimeter of the garden?
Two numbers differ by 7, and the sum of their squares is 29. Find the numbers.
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?
A regional candy factory sells a guava roll at a price of $48, the monthly fixed costs amount to $125,000 and the variable cost for making a guava roll is $28. Determine: a) The equation of the total income from the production of guava rolls.
A vaccine has a 90% probability of being effective in preventing a certain disease. The probability of getting the disease if a person is not vaccinated is 50%. In a certain geographic region, 60% of the people get vaccinated. If a person is selected at random from this region, find the probability that he or she will contract the disease. (4 Points)
In an audience of 4000 people, 2 people are chosen, at random, to appear on stage. How many ways can the people be chosen?
Which of the methods below can be used to workout 95% of an amount? a. Dividing the amount 100 and multiply by 95 b. Working out 5% of the amount and taking it away from the full amount c. Dividing 95 by 100 and multiplying the answer by the amount d. Dividing the amount by 95 and then multiply by 100
Buffalo Company makes and sells shampoo. Each unit requires $1.40 labor costs, material costs per unit are $0.90 and other variable costs are $0.30. It sells shampoo for $4.45 to retailers. Fixed costs are $15,000. It sold 25,000 units in the current month. What is the Break-Even point in units? What is the Break-Even point in dollars? What is the contribution margin of Buffalo Company?
Calculate the area of the parallelogram with adjacent vertices (1,4, −2), (−3,1,6) 𝑦 (1, −2,3)
a) 6x − 5 > x + 20
To verify that a 1 kg gold bar is actually made of pure gold, a dynamometer is used to record the weight of the bar submerged in water and out of water. a) What would be the value of the weight of the ingot recorded by the dynamometer out of the water? b) What magnitude of thrust does the ingot receive when it is submerged? c) What would the weight of the ingot have to be when it is submerged? Data Pagua = 1000 kg/m³ Pagua= 19300 kg/m³
Identify the slope and y intercept y=11+2/3x
did an analysis of dropout from the nursing faculty at the Universidad Veracruzana. With a poblation of 122 students, it turned out that according to the gender data, the female sex predominates with 82%, and the male sex male is found with 12%. The main factors why students drop out are, first of all, "Not "re-enrolled" at 49%, second place "Personal reasons" at 20%, third place "change of school" in 11%, "lack of documents" and "economic reasons" in 7%, change of residence and lack of social service in 3%. Of this sample, how many students dropped out for other reasons?
t+72/t=-17
(3.1x10^3g^2)/(4.56x10^2g)
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.

You might be interested in