The price of a floor tile is $3 per square foot, and the cost of shipping...

The price of a floor tile is $3 per square foot, and the cost of shipping is $20. You are adjusting the size of your bathroom according to the space availability. You would like to estimate the rate of change of cost for flooring that you expect when you change the size of the square bathroom of current length 10 feet. Assume x to be the length of a square shaped bathroom.Include units in all parts.

a. Calculate the average rate of change of cost when you change your bathroom from 10 feet to 12 feet long.

b. Calculate the instantaneous rate of change of cost at length 10 feet.

c. If the cost of shipping also depends on the length according to $20(1+sinx), what is the instantaneous change of cost at length 10 feet.

Solutions

Expert Solution

a.Calculation of the average rate of change of cost:

The average rate of change of cost=the average rate of output value/the average rate of input value

= 12/10

=1.2

b.Calculation of the instantaneous rate of change of cost:

the instantaneous rate of change of cost=d/dx(x=10)

c.Calculation of the instantaneous rate of change of cost:

the instantaneous rate of change of cost=a(20(1+sin(x)))/ax where x=10

=20 cos(10)

Rahul Sunny answered 1 year ago

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