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.

The marginal cost function is the derivative of the total cost function. It represents the cost of producing one more unit. In this case, the marginal cost function is given by C'(x) = 3x^2 - 200x + 1500.

To find the increase in cost if production is increased from 90 to 100 units, we need to integrate the marginal cost function from 90 to 100.

∫ from 90 to 100 (3x^2 - 200x + 1500) dx

= [x^3 - 100x^2 + 1500x] from 90 to 100

= (100^3 - 100100^2 + 1500100) - (90^3 - 10090^2 + 150090)

= (1000000 - 1000000 + 150000) - (729000 - 810000 + 135000)

= 50000 - 216000

= -166000 rupees

The negative sign indicates a decrease in cost, not an increase. So, if production is increased from 90 to 100 units, the cost will decrease by 166000 rupees.