HSC Commerce (English Medium) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

State whether the following statement is True or False.

Corr (x, y) = Corr (y, x)

State whether the following statement is True or False.

b_xy and b_yx are independent of change of origin and scale. 

‘r’ is regression coefficient of Y on X

State whether the following statement is True or False.

b_yx is correlation coefficient between X and Y

State whether the following statement is True or False.

If u = x - a and v = y - b then b_xy = b_uv 

State whether the following statement is True or False.

If u = x - a and v = y - b then r_xy = r_uv 

A manufacturing firm produces two types of gadgets A and B, which are first processed in the foundry and then sent to machine shop for finishing. The number of man hours of labour required in each shop for production of A and B and the number of man hours available for the firm are as follows:

Profit on the sale of A is ₹ 30 and B is ₹ 20 per unit. Formulate the L.P.P. to have maximum profit.

In a cattle breeding firm, it is prescribed that the food ration for one animal must contain 14, 22, and 1 unit of nutrients A, B, and C respectively. Two different kinds of fodder are available. Each unit weight of these two contains the following amounts of these three nutrients:

The cost of fodder 1 is ₹ 3 per unit and that of fodder ₹ 2 per unit. Formulate the L.P.P. to minimize the cost.

A company manufactures two types of chemicals A and B. Each chemical requires two types of raw material P and Q. The table below shows number of units of P and Q required to manufacture one unit of A and one unit of B.

The company gets profits of ₹ 350 and ₹ 400 by selling one unit of A and one unit of B respectively. Formulate the problem as L.P.P. to maximize the profit.

A printing company prints two types of magazines A and B. The company earns ₹ 10 and ₹ 15 on magazines A and B per copy. These are processed on three machines I, II, III. Magazine A requires 2 hours on Machine I, 5 hours on Machine II and 2 hours on Machine III. Magazine B requires 3 hours on Machine I, 2 hours on Machine II and 6 hours on Machine III. Machines I, II, III are available for 36, 50, 60 hours per week respectively. Formulate the Linear programming problem to maximize the profit.

A manufacturer produces bulbs and tubes. Each of these must be processed through two machines M₁ and M₂. A package of bulbs requires 1 hour of work on Machine M₁ and 3 hours of work on M₂. A package of tubes requires 2 hours on Machine M₁ and 4 hours on Machine M₂. He earns a profit of ₹ 13.5 per package of bulbs and ₹ 55 per package of tubes. If maximum availability of Machine M₁ is 10 hours and that of Machine M₂ is 12 hours, then formulate the L.P.P. to maximize the profit.

A company manufactures two types of fertilizers F₁ and F₂. Each type of fertilizer requires two raw materials A and B. The number of units of A and B required to manufacture one unit of fertilizer F₁ and F₂ and availability of the raw materials A and B per day are given in the table below:

By selling one unit of F₁ and one unit of F₂, company gets a profit of ₹ 500 and ₹ 750 respectively. Formulate the problem as L.P.P. to maximize the profit.

Solve the following L.P.P. by graphical method:

Maximize: Z = 4x + 6y

Subject to 3x + 2y ≤ 12, x + y ≥ 4, x, y ≥ 0.

Choose the correct alternative :

Which of the following is correct?

Objective function of LPP is ______.

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Of all the points of the feasible region the optimal value of z is obtained at a point

Choose the correct alternative :

Feasible region; the set of points which satify.

Choose the correct alternative :

Solution of LPP to minimize z = 2x + 3y st. x ≥ 0, y ≥ 0, 1≤ x + 2y ≤ 10 is

Choose the correct alternative :

The corner points of the feasible region given by the inequations x + y ≤ 4, 2x + y ≤ 7, x ≥ 0, y ≥ 0, are

Choose the correct alternative :

The corner points of the feasible region are (0, 0), (2, 0), `(12/7, 3/7)` and (0,1) then the point of maximum z = 7x + y