HSC Commerce (English Medium) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Solve the following problem :

A Company produces mixers and processors Profit on selling one mixer and one food processor is ₹ 2000 and ₹ 3000 respectively. Both the products are processed through three machines A, B, C The time required in hours by each product and total time available in hours per week on each machine are as follows:

How many mixers and food processors should be produced to maximize the profit?

Solve the following problem :

A person makes two types of gift items A and B requiring the services of a cutter and a finisher. Gift item A requires 4 hours of cutter's time and 2 hours of finisher's time. B requires 2 hours of cutters time, 4 hours of finishers time. The cutter and finisher have 208 hours and 152 hours available times respectively every month. The profit of one gift item of type A is ₹ 75 and on gift item B is ₹ 125. Assuming that the person can sell all the items produced, determine how many gift items of each type should be make every month to obtain the best returns?

Solve the following problem :

A firm manufacturing two types of electrical items A and B, can make a profit of ₹ 20 per unit of A and ₹ 30 per unit of B. Both A and B make use of two essential components, a motor and a transformer. Each unit of A requires 3 motors and 2 transformers and each unit of B requires 2 motors and 4 transformers. The total supply of components per month is restricted to 210 motors and 300 transformers. How many units of A and B should be manufacture per month to maximize profit? How much is the maximum profit?

Calculate the cost of living index in problem 

Calculate the cost of living index in problem

Calculate the cost of living index in problem

The cost of Living Index Number using Aggregate Expenditure Method is given by ______.

Four new machines M₁, M₂, M₃ and M₄ are to be installed in a machine shop. There are five vacant places A, B, C, D and E available. Because of limited space, machine M₂ cannot be placed at C and M₃ cannot be placed at A. The cost matrix is given below:

Find the optimal assignment schedule.

A company has a team of four salesmen and there are four districts where the company wants to start its business. After taking into account the capabilities of salesmen and the nature of districts, the company estimates that the profit per day in rupees for each salesman in each district is as below:

Find the assignment of salesman to various districts which will yield maximum profit.

In the modification of a plant layout of a factory four new machines M₁, M₂, M₃ and M₄ are to be installed in a machine shop. There are five vacant places A, B, C, D and E available. Because of limited space, machine M₂ cannot be placed at C and M₃ cannot be placed at A. The cost of locating a machine at a place (in hundred rupees) is as follows.

Find the optimal assignment schedule.

Fill in the blank :

An assignment problem is said to be unbalanced when _______.

Fill in the blank :

When the number of rows is equal to the number of columns then the problem is said to be _______ assignment problem.

Fill in the blank :

If the given matrix is not a _______ matrix, the assignment problem is called an unbalanced problem.

Fill in the blank :

A dummy row(s) or column(s) with the cost elements as _______ is added to the matrix of an unbalanced assignment problem to convert into a square matrix.

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.