HSC Commerce (English Medium) इयत्ता १२ वी - Maharashtra State Board Question Bank Solutions

Maximization assignment problem is transformed to minimization problem by subtracting each entry in the table from the _______ value in the table.

Fill in the blank :

In an assignment problem, a solution having _______ total cost is an optimum solution.

Fill in the blank :

In maximization type, all the elements in the matrix are subtracted from the _______ element in the matrix.

To convert the assignment problem into a maximization problem, the smallest element in the matrix is deducted from all other elements.

State whether the following is True or False :

The purpose of dummy row or column in an assignment problem is to obtain balance between total number of activities and total number of resources.

State whether the following is True or False

In number of lines (horizontal on vertical) > order of matrix then we get optimal solution.

Solve the following problem :

Solve the following assignment problem to maximize sales:

Solve the following problem :

The estimated sales (tons) per month in four different cities by five different managers are given below:

Find out the assignment of managers to cities in order to maximize sales.

Use quantifiers to convert the given open sentence defined on N into a true statement

n² ≥ 1

Use quantifiers to convert the given open sentence defined on N into a true statement.

3x – 4 < 9

Use quantifiers to convert the given open sentence defined on N into a true statement.

Y + 4 > 6

Divide the number 20 into two parts such that their product is maximum

A rod of 108 m long is bent to form a rectangle. Find it’s dimensions when it’s area is maximum.

A metal wire of 36 cm long is bent to form a rectangle. By completing the following activity, find it’s dimensions when it’s area is maximum.

Solution: Let the dimensions of the rectangle be x cm and y cm.

∴ 2x + 2y = 36

Let f(x) be the area of rectangle in terms of x, then

f(x) = `square`

∴ f'(x) = `square`

∴ f''(x) = `square`

For extreme value, f'(x) = 0, we get

x = `square`

∴ f''`(square)` = – 2 < 0

∴ Area is maximum when x = `square`, y = `square`

∴ Dimensions of rectangle are `square`

By completing the following activity, examine the function f(x) = x³ – 9x² + 24x for maxima and minima

Solution: f(x) = x³ – 9x² + 24x

∴ f'(x) = `square`

∴ f''(x) = `square`

For extreme values, f'(x) = 0, we get

x = `square` or `square`

∴ f''`(square)` = – 6 < 0

∴ f(x) is maximum at x = 2.

∴ Maximum value = `square`

∴ f''`(square)` = 6 > 0

∴ f(x) is maximum at x = 4.

∴ Minimum value = `square`

Choose the correct alternative:

`intx^(2)3^(x^3) "d"x` =

`int ("d"x)/(x - x^2)` = ______

Choose the correct alternative:

`int ("d"x)/((x - 8)(x + 7))` =

`int(x + 1/x)^3 dx` = ______.

`int 1/x  "d"x` = ______ + c