HSC Commerce: Marketing and Salesmanship 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions

In a factory, for production of Q articles, standing charges are ₹500, labour charges are ₹700 and processing charges are 50Q. The price of an article is 1700 - 3Q. Complete the following activity to find the values of Q for which the profit is increasing.

Solution: Let C be the cost of production of Q articles.

Then C = standing charges + labour charges + processing charges

∴ C = `square` 

Revenue R = P·Q = (1700 - 3Q)Q = 1700Q- 3Q²

Profit `pi = R - C = square`

 Differentiating w.r.t. Q, we get

`(dpi)/(dQ) = square`

If profit is increasing , then `(dpi)/(dQ) >0`

∴ `Q < square` 

Hence, profit is increasing for `Q < square` 

Find `dy/dx` if, x = `e^(3t)`, y = `e^sqrtt`

If log (x + y) = log (xy) + a then show that, `dy/dx = (−y^2)/x^ 2`

Find `dy/dx if , x = e^(3t) , y = e^sqrtt`

If log (x+y) = log (xy) + a then show that, `dy/dx= (-y^2)/(x^2)`

Following table shows the all India infant mortality rates (per '000) for years 1980 to 2010:

Fit the trend line to the above data by the method of least squares.

Evaluate.

`int (5x^2 - 6x + 3) / (2x -3) dx`

Find `dy / dx` if, x = `e^(3t), y = e^sqrt t` 

Solve the following.

If log(x + y) = log(xy) + a then show that, `dy/dx = (-y^2)/x^2`

Find `dy/dx` if, x = e^3t, y = `e^sqrtt`

Find `dy/dx` if, `x = e^(3t), y = e^sqrtt`

Find `dy/dx` if, `x = e^(3t), y = e^(sqrtt)`

If log(x + y) = log(xy) + a then show that, `dy/dx = (-y^2)/x^2`

If log(x + y) = log(xy) + a then show that, `dy/dx = (−y^2)/x^2`

If log(x + y) = log(xy) + a then show that, `dy/dx=(-y^2)/x^2`

Find `dy/dx"if", x= e^(3t), y=e^sqrtt`

If log(x + y) = log(xy) + a then show that, `dy/dx = (-y^2)/x^2`

Find `dy/(dx)  "if" , x = e^(3t), y = e^sqrtt`. 

Find `dy/dx` if, `x = e^(3t), y = e^(sqrtt)`

Evaluate.

`int (5x^2 - 6x + 3)/(2x - 3)dx`