Different Types of Linear Programming Problems

A dietician has to develop a special 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 maximize the amount of vitamin $A$ in the diet? What is the maximum amount of vitamin $A$?

A farmer mixes two brands $P$ and $Q$ of cattle feed. Brand $P,$ costing $\mathrm{₹}\mathrm{}250$ per bag contains $3$ units of nutritional element $A,2.5$ units of element $B$ and $2$ units of element $C.$ Brand $Q$ costing $\mathrm{₹}\mathrm{}200$ per bag contains $1.5$ units of nutritional elements $A,11.25$ units of element $B,$ and $3$ units of element $C.$ The minimum requirements of nutrients $A,B$ and $C$ are $18$ units, $45$ units and $24$ units respectively. Determine the number of bags of each brand which should be mixed in order to produce a mixture having a minimum cost per bag? What is the minimum cost of the mixture per bag?

An aeroplane can carry a maximum of $200$ passengers. A profit of $\mathrm{₹}\mathrm{}1000$ is made on each executive class ticket and a profit of $\mathrm{₹}\mathrm{}600$ is made on each economy class ticket. The airline reserves at least $20$ seats for executive class. However, at least $4$ times as many passengers prefer to travel by economy class than by the executive class. Determine how many tickets of each type must be sold in order to maximize the profit for the airline. What is the maximum profit?

A fruit grower can use two types of fertilizer in his garden, brand $P$ and brand $Q.$ The amounts (in $\mathrm{k}\mathrm{g}$) 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 $240\mathrm{}\mathrm{k}\mathrm{g}$ of phosphoric acid at least $270\mathrm{}\mathrm{k}\mathrm{g}$ of potash and at most $310\mathrm{}\mathrm{k}\mathrm{g}$ of chlorine.
If the grower wants to minimize 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?

There are two types of fertilizers $F_1$ and $F_2.F_1$ consists of $10\%$ nitrogen and $6\%$ phosphoric acid and $F_2$ consists of $5\%$ nitrogen and $10\%$ phosphoric acid. After testing the soil conditions, a farmer finds that she needs at least $14\mathrm{}\mathrm{k}\mathrm{g}$ of nitrogen and $14\mathrm{}\mathrm{k}\mathrm{g}$ of phosphoric acid for her crop. If $F_1$ cost $\mathrm{₹}\mathrm{}6/\mathrm{k}\mathrm{g}$ and $F_2$ costs $\mathrm{₹}\mathrm{}5/\mathrm{k}\mathrm{g},$ determine how much of each type of fertilizer should be used so that nutrient requirements are met at a minimum cost. What is the minimum cost?

A company manufactures two types of novelty souvenirs made of plywood. Souvenirs of type $A$ require $5$ minutes each for cutting and $10$ minutes each for assembling. Souvenirs of type $B$ require $8$ minutes each for cutting and $8$ minutes each for assembling. There are $3$ hours $20$ minutes available for cutting and $4$ hours of assembling. The profit is $\mathrm{₹}\mathrm{}5$ each for type $A$ and $\mathrm{₹}\mathrm{}6$ each for type $B$ souvenirs. How many souvenirs of each type should the company manufacture in order to maximize the profit?

Which role do entrepreneurs play in the allocation of resources?

What motivates entrepreneurs to start new businesses and contribute to economic development?

Which type of distribution channel involves selling products directly from the manufacturer to the consumer?

What is the primary role of intermediaries in a distribution channel?

Which plan period was known for the introduction of the Decentralized Planning in India?

Which pricing strategy involves charging different prices to different customer groups?

Which of the following is a characteristic of Cost-Plus Pricing?

Which pricing strategy involves setting a high price to create a perception of high quality?

What is the definition of Penetration Pricing?

Which government program focuses on providing skill development and entrepreneurship among the youth of India?

Which program aims at skill development of rural youth to enhance their employability?

Which government scheme primarily aims at providing employment opportunities in rural areas?

What does LPG stand for in the context of Indian economic reforms?

Which conflict resolution strategy involves both parties working together to find a mutually beneficial solution?