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.

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.]

Let y=3x.(x+a)/(x+b)+5 [a and b are positive constants and a gt b ] be the total cost for x unit of output of a commodity. Show that the marginal cost falls continuosly as the output increases.

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.

A firm produces x units of output per week at a total cost of Rs. ((1)/(3)x^(3)-x^(2)+5x+3) .Find the output levels at which the marginal cost, the average variable cost attain their respective minima.

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.

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 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.

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.

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 ?

The cost of fuel of an engine varies as the square of its velocity and the cost of fuel is ₹ 48 per hour when the velocity is 16 km per hour. If other expenses be ₹ 300 per hour, then show that the most economical velocity for a journey of a given distance is 40 km per hour.