M L Aggarwal Solutions for Chapter: Linear Programming, Exercise 3: CHAPTER TEST

A company manufactures two types of screws A and B. All the screws have to pass through a threading machine and a slotting machine. A box of type A screws requires $2$ minutes on threading machine and $3$ minutes on slotting machine. A box of type B screws requires $8$ minutes of threading on the threading machine and $2$ minutes on the slotting machine.

In a week, each machine is available for $60$ hours. On selling these screws, the company gets a profit of Rs $100$per box on type A screw and Rs $170$ per box on type B screws. How many boxes of screws of each type should be manufactured to get maximum profit. From it as an L.P.P. and solve graphically. 

A manufacturer produces two models of bikes-model X and model Y. Model X takes a $6$ man-hours to make per unit, while model Y takes $10$ man-hours per unit. There is a total of $450$ man-hours available per week. Handling and marketing costs are Rs $2000$ and Rs $1000$ per unit for Models X and Y respectively.

The total funds available for these purposes are Rs $80000$ per week. Profit per unit for models X and Y are Rs $1000$ and Rs $600$ respectively.

How many bikes of each model should the manufacturer produce so as to yield a maximum profit? Form and L.P.P and Solve graphically. 

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 products a unit of B. A market survey shows that maximum $70$ units of A and $125$ units of B can be sold. If the profit is $20$ per unit for the product A and $15$ per unit for the product B, how many units of each product should be sold to maximise profit?

A manufacturer of electronic circuit has a stock of $200$ resistors, $120$ transistors and $150$ capacitors and is producing two types of circuits A and B. Type A requires $20$ resistors, $10$ transistors and $10$ capacitors. Type B requires $10$ resistors, $20$ transistors and $30$ capacitors. If the profit on type A circuit is $40$ and that on type B circuit is $90$. How many circuits of type A and of type B should be produced by the manufacturer to maximise his profit?

Formulate an L.P.P. and solve it graphically.

A furniture firm manufactures chairs and tables, each requiring the use of three machines A, B and C. Production of one chair requires $2$ hours on machine A, $1$ hour on machine B and $1$ hour on machine C. Each table requires $1$ hour each on machine A and B and $3$ hours on machine C. The profit obtained by selling one chair is $30$ while by selling one table is $60$. The total time available per week on machine A is $70$ hours, on machine B is $40$ hours and on machine C is $90$ hours. How many chairs and tables should be made per week so as to maximise the profit?

Formulate the problem as L.P.P. and solve it graphically.

Suppose every gram of wheat provides $0.1$ g of proteins and $0.25$ g of carbohydrates, and the corresponding values for rice are $0.05$ g and $0.5$ g respectively. Wheat costs $20$ and rice $30$ per kilogram. The minimum daily requirement of an average man for proteins and carbohydrates is $50$ g and $200$ g respectively. In what quantities should wheat and rice be mixed in the daily diet to provide the minimum daily requirements of proteins and carbohydrates at minimum cost? What is the minimum cost?

To maintain one's health, a person must fulfil certain minimum daily requirements for the following three nutrients-calcium, protein and calories. His diet consists of only food items I and II whose prices and nutrient contents are shown below :
 

Find the combination of food items so that the cost may be minimum. 

Two godowns A and B have a grain storage capacity of $100$ quintals and $50$ quintals respectively. They supply to $3$ ration shops D, E and F, whose requirements are $60, 50$ and $40$ quintals respectively. The costs of transportation per quintal from the godowns to the shops are given in the following table:

How should the supplies be transported in order that the transportation cost is minimum? What is the minimum cost?