A producer has 30 and 17 units of labour and capital respectively which he can use to produce two of goods X and Y. To produce one unit X, 2 units of labour and 3 units of capital are required. Similarly, 3 units of labour and 1 unit of capital is required to produce one unit of Y. If X and Y are priced at Rs. 100 and Rs. 120 per unit respectively to should be producer use his resources to maximize the total revenue?

A manufacturer considers that men and women workers are equally efficient and so he pays them at the same rate. He has 30 and 17 units of workers (male and female) and capital respectively, which he uses to produce two types of goods A and B. To produce one unit of A, 2 workers and 3 units of capital are required while 3 workers and 1 unit of capital is required to produce one unit of b. If A and B are priced at Rs. 100 and Rs. 120 per unit respectively, how should he use his resources to maximize the total revenue? Form the above as an LPP and solve graphically. Do you agree with this view of the manufacture that men and women workers are equally efficient and so should be paid at the same rate?

Two vectors have magnitudes 3 unit and 4 unit respectively. What should be the angel between them if the magnitude of the resultant ils a. 1 unit, b. 5 unit and c. 7 unit.

A farm is engaged in breeding pigs. The pigs are fed on various products grown on the farm. In view of the need to ensure certain nutrient constituents (call them X,Y and Z), it is necessary to buy two additional products, say, A and B. One unit of product A contains 36 units of X, 3 units of Y, and 20 units of Z. One unit of product B contains 6 units of X, 12 units of Y and 10 units of Z. The minimum requirement of X, Y and Z is 108 units respectively. Product A costs LRs. 20 per unit and product B costs Rs. 40 per unit. Formulate the above as a linear programming problem to minimize the total cost, and solve the problem by using graphical method.

A company sells two different products, A and B. The two products are produced in a common production process, which has a total capacity of 500 man-hours. It takes 5 hours to produce a unit of A and 3 hours to produce a unit of B. The market has been surveyed and company officials feel that the maximum number of units of A that can be sold is 70 and that, for B is 125. If the profit is Rs. 20 per unit for the product A and Rs. 15 per unit for the product B, how many units of each product should be sold to maximize profit?

A company sells two different products A and B. The two products are produced in a common production process and are sold in two different markets. The production process has a total capacity of 45000 man-hours. It takes 5 hours to produce a unit of A and 3 hours to produce a unit of B. The market has been surveyed and company officials feel that the maximum number of units of A that can be sold is 7000 ad that of B is 10,000. If the profit is Rs. 60 per unit for the product A and Rs. 40 per unit for the product B, how many units of each product should be sold to maximize profit? Formulate the problem as LPP.

Two vectors have magnitudes 3 unit and 4 unit respectively. What should be the angel between them if the magnitude of the resultant is (a). 1 unit (b). 5 unit and (c). 7 unit.

The prices of three commodities P ,\ Q ,\ a n d\ R are Rs x ,\ y\ a n d\ z per unit respectively. A purchases 4 units of R and sells 3 unit of P and 5 units of Qdot B purchases 3 units of Q and sells 2 units of P and 1 unit of Rdot C purchases 1 unit of P and sells 4 units of Q and 6 units of Rdot In the process A ,\ B\ a n d\ C earn Rs 6000, 5000 and 13000 respectively. If selling the units is positive earning and buying the units is negative earnings, find the price per unit of three commodities by using matrix method.

A carpenter has 90, 80 and 50 running feet respectively of teak wood, plywood and rosewood which is used to produce product A and product B. Each unit of product A required 2, 1 and 1 running feet and each unit of product B requires 1, 2 and 1 running feet of teak wood, plywood and rosewood respectively. If product A is sold for Rs 48 per unit and product B is sold forRs 40 per unit, how many units of product A and product B should be produced and sold by the carpenter, in order to obtain the maximum gross income, Formulate the above as a Linear Programming Problem and solve it, indicating clearly the feasible region in the graph.

A vector has x component of -25.0 units and y component of 40.0 units find the magnitude and direction of the vector.

A dietician has to develop a social diet using two foods P and Q. Each packet (containing 30 g) of food P contains 12 units of calcium, 4 units of iron, 6 units of cholesterol and 6 units of vitamin A. Each packet of the same quantity of food Q contains 3 units of calcium, 20 units of iron, 4 units of cholesterol and 3 units of vitamin A. The diet requires atleast 240 units of calcium, atleast 460 units of iron and at most 300 units of cholesterol. How many packets of each food should be used to minimise the amount of vitamin A in the diet? What is the minimum amount of vitamin A?