For any student, it is extremely important to understand the concepts associated with linear programming as well as the various tools associated with this process.

Here are some of the problems that would surely help you in getting a detailed idea of this whole procedure.

**Sum 1: **

It is taken that a tailor has 120 sq, m of woolen cloth with him, as well as 80 sq.m of cotton cloth. If a suit requires 3 sq.m of woolen cloth and 1 sq.m of cotton cloth with a dress requiring 2 sq.m of both, then what would be the LPP given that income is to be maximized. It is taken that dress costs $400, and suit costs $500.

**Sum 2: **

It is found that a particular entrepreneur makes chairs and tables only. In this given situation, it can be seen that a table requires 2 hours on m/c B, while 5 hours on m/c A. also, it is found that the chair requires, 6 hours on m/c B and 2 hours on m/c A on a per day basis.

It is given that profit for a table is taken at $5, while profit for the chair is at $1. So, now frame a linear programming curve to depict the regular production that is associated with this item and what are the maximum profits that are gained?

**Sum 3: **

It is found that a particular company produces 2 goods, X and Y. If it is taken that profit associated with product Y is $15, while profit associated with product X is $10. It is also taken that total sale of both the units should not be less than $400, while for Good X, 40 units are manufactured, while for Good Y only 20 units are manufactured.

If it is seen that the market demand for both of these products amount to $40 units, then what should be that optimum amount of units that should be manufactured to get maximum profit for the company. This problem is to be explained in a graphical manner with LPP.

**Sum 4: **

It is seen that a pharmaceutical company has 100 kg of Product X, 180 kg of Product Y and 120 kg of Product Z. The products that would be made with the help of these goods are 5-l 0-5; 5-5-10 and 20-5-1 0, which provide number that are represented by percentages of X, Y,Z.

Given that the costs associated with these products are $80 for product X, $20 for product Y, $50 for product Z, the selling price of these products are taken as $ 40.5, $ 43 and $ 45 per kg. If the capacity restriction of the company is at 30kg, and for the product it is at 5-10-5, so what should be the production rate to get maximum profit on a monthly basis?

**Sum 5: **

Let us consider two buses of two categories: Simple type and the Semi-Deluxe type. The Simple type requires 2 mechanics for its servicing, whereas it can carry a total of 40 passengers. In case of Semi-deluxe bus, there are 3 mechanics required for servicing and it can carry a total amount of 60 people.

If it is taken that a particular company can only provide 12 mechanics and transport 300 people on a regular basis, how would the problem be formulated in LPP? It is also given that costs are minimized and for the Simple bus it is $ 1,20,000, while for the Semi deluxe bus it is kept at $ 1 ,50,000.

**Sum 6: **

Let us take a company that has 2 mines.

Mine X produces:5 tonlow grade ore, 3 ton medium grade ore, and 1 tonhigh grade ore.

Mine Y produces: 2 ton of ore of each grade.

The company requires 200 tons of lower quality ore, 160 ton of medium quality ore and 800 tons of high grade ore. If it is taken that Rs 200 is spent on operation of each of the ores, then what would be the total number of days that have to be used for getting the maximum output with minimal cost?

Once these queries are solved, students will get a better grip of the subject.