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? (

Brand: MathMaster
Rating: 4.9 (189 reviews)

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

68 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)

What is the standard deviation of a dataset consisting of [2, 4, 6, 8]?

Question: Solve the expression (x + 3)(2x - 5)(4x + 1) using the distributive property.

Math question: Solve the quadratic equation: 2x² + 5x - 3 = 0.

New questions in Mathematics

Calculate to represent the function whose graph is a line that passes through the points (1,2) and (−3,4). What is your slope?

Additionally, the boss asked Armando to determine how many toy sales branches he would have in the fifteenth year, knowing that the first year they started with two branches, by the second they already had 5 branches and, by the third year, they had 8 branches. From the above, determine the number of branches it will have for the fifteenth year.

Two numbers differ by 7, and the sum of their squares is 29. Find the numbers.

(2b) to the 1/4th power. Write the expression in radical form.

2.3/-71.32

The durability of a tire of a certain brand is a Normal random variable with an average of 64,000 km and a standard deviation of 9,000 km. Assuming independence between tires, what is the probability that the 4 tires on a car will last more than 58,000 km?

determine the polynomial F of degree 2 that interpolates. f at points (0;1) (2;5) (4;6). calculate F(0.8). Note: Using the polynomial expression with difference operator.