The marginal cost of manufacturing x yards of a certain fabric is C'(x) = 3 − 0.01x + 0.000009x2 (in dollars per yard). Find the increase in cost if the production level is raised from 2000 yards to 4000 yards.

(c) Compare C'(400) with the cost of manufacturing the 401st yard of fabric. (Round your answers to four decimal places.)The cost of manufacturing the 401st yard of fabric is C(401) − C(400) = − 22,400 ≈ , which is approximately

Juli wants to buy 2.5 yards of fabric for a project. The fabric costs $5.88 per yard. About how much will the fabric for Juli's project cost?

The cost (in dollars) of producing x units of a certain commodity is C(x) = 7000 + 10x + 0.05x2.(a) Find the average rate of change of C with respect to x when the production level is changed from x = 100 to the given value. (Round your answers to the nearest cent.)(i)    x = 102$ per unit(ii)    x = 101$ per unit(b) Find the instantaneous rate of change of C with respect to x when x = 100. (This is called the marginal cost.)

The marginal cost function for producing x units is 3x2 – 200x +1500 rupees. Find the increase in cost if production is increasedfrom 90 to 100 units.

A consumer has an income of $10,000 to spend on two goods, X and Y, where the price ofgood X is $500 per unit, and the price of good Y is $1 per unit. The marginal rate ofsubstitution is given by the formula Y/X. How many units of good Y does this consumeroptimally c