Linear Programm...

In linear programming feasible region (or solution region) for the problem is

In a LPP if the objective function Z = ax + by has the same maximum value on two corner points of the feasible region, then every point on the line segment joining these two points give the same

A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftman ’s time in its making while a cricket bat takes 3 hour of machine time and 1 hour of craftman ’s time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman ’s time. What number of rackets and bats must be made if the factory is to work at full capacity?

A fruit grower can use two types of fertilizer in his garden, brand P and brand Q. The amounts (in kg) of nitrogen, phosphoric acid, potash, and chlorine in a bag of each brand are given in the table. Tests indicate that the garden needs at least 240 kg of phosphoric acid, at least 270 kg of potash and at most 310 kg of chlorine.If the grower wants to minimise the amount of nitrogen added to the garden, how many bags of each brand should be used? What is the minimum amount of nitrogen added in the garden? should the delivery be scheduled in order that the transportation cost is minimum? 

In a LPP, the linear inequalities or restrictions on the variables are called

In linear programming infeasible solutions

In linear programming problems the function whose maxima or minima are to be found is called

A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftman ’s time in its making while a cricket bat takes 3 hour of machine time and 1 hour of craftman ’s time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman ’s time. If the profit on a racket and on a bat is Rs 20 and Rs 10 respectively, find the maximum profit of the factory when it works at full capacity?

A fruit grower can use two types of fertilizer in his garden, brand P and brand Q. The amounts (in kg) of nitrogen, phosphoric acid, potash, and chlorine in a bag of each brand are given in the table. Tests indicate that the garden needs at least 240 kg of phosphoric acid, at least 270 kg of potash and at most 310 kg of chlorine.

If the grower wants to maximise the amount of nitrogen added to the garden, how many bags of each brand should be added? What isthe maximum amount of nitrogen added?

Determine the maximum value of Z = 3x + 4y if the feasible region (shaded) for a LPP is shown in Figure above. 

In linear programming, optimal solution

In linear programming problems the optimum solution

A manufacturer produces nuts and bolts. It takes 1 hour of work on machine A and 3 hours on machine B to produce a package of nuts. It takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts. He earns a profit of Rs17.50 per package on nuts and Rs 7.00 per package on bolts. How many packages of each should be produced each day so as to maximise his profit, if he operates his machines for at the most 12 hours a day?

A toy company manufactures two types of dolls, A and B. Market tests and available resources have indicated that the combined production level should not exceed 1200 dolls per week and the demand for dolls of type B is at most half of that for dolls of type A. Further, the production level of dolls of type A can exceed three times the production of dolls of other type by at most 600 units. If the company makes profit of Rs 12 and Rs 16 per doll respectively on dolls A and B, how many of each should be produced weekly in order to maximise the profit?

Feasible region (shaded) for a LPP is shown in Figure. Maximize Z = 5x + 7y.