The marginal cost of a commodity is given by Rs `(27-32x+9x^(2))` , where x is the output. Find the total cost and average cost function, given that the initial cost is RS 50.

Suppose the marginal cost of a product is given by RS(10+24x-3x^(2)) , where x is the number of units produced. It the fixed cost is known to be RS 40, find the total cost function and the average cost function.

The marginal cost function of manufacturing x pairs of shoes is RS(6+10x-6x^(2)) . The total cost of producing a pair of shoes is RS 12. Find the total and average cost functions.

If y is the total cost of x units of output and it is given that marginal cost equals average cost, show that the average cost function is constant.

If the marginal function for x units of output is given by (6)/((x+2)^(2))+5 , find the total revenue function and the demand law.

The cost c of manufacturing a certain article is given by the formula , c=5+(48)/(x)+3x^(2) , where x is the number of articles manufactured . Find the minimum value of c .

A firm produces x tonnes of output at a total cost of Rs. R where R=(1)/(10)x^(3)-5x^(2)+10x+5 . At what level of output will the marginal cost and the average variable cost attain their respective minima ?

Let y=3x. (x+7)/(x+5)+4 be the total cost for x units of output of a product. Show that the marginal cost falls continuously as the output increases. [Note that the marginal cost of a product is the rate of change in cost for unit change in the output.]

Find the minima of the given function: h(x) = x^(2) +x

The total cost C(x) in Rupees, associated with the production of x units of an item is given by C(x) = 0.005x^(3)- 0.02 x^(2)+30x+5000 Find the marginal cost when 3 units are produced, where by marginal cost we mean the instantaneous rate of change of total cost at any level of output.

If the marginal revenue function is (15-2x-x^(2)) , find total revenue function and the demand function (x being the number units sold).