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? $Jett 4.7 52 Answers a$ 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.

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