A manufacturer produces two types of steel trunks. He has two machine A and B. For completing, the first type of the trunk requires 3 hours on machine A and 2 hours on machine B, whereas the second type of the trunk requires 3 hours on machine A and 3 hours on machine B. Machines A and B can work at the most for 18 hours and 14 hours per day respectively. He earns a profit of Rs.30 andRs.40 per trunk of the first type and second type respectively. How many trunks of the each type must he make each day to make maximum profit?

Reshma wishes to mix two types of food P and Q in such a way that the Vitamin contents of the mixture contain at least 8 units of vitamin A and 11 units of vitamin B. Food P costs Rs.60/kg and Food Q costs Rs.80/kg. Food P contains 3 units 1 kg of vitamin A and 5 units 1 kg of vitamin B while food Q contains 4 units 1 kg of vitamin A and 2 units 1 kg of vitamin B. Determine the minimum cost of the mixture.

One kind of the cake requires 200 g of flour and 25 g of fat, and another kind of cake requires 100 g of flour and 50 g of fat. Find the maximum number of cakes which can be made from 5 kg of flour and 1 kg of fat assuming that there is no shortage of other ingredients used in making the cakes?

A manufacturer makes two types of toys A and B. Three machines are needed for this purpose and the time (min) required for each toy on the machine is given below:

Each machine is available for a maximum of 6 hours/day. If the profit on each toy of type A is Rs.7.50 and for B is Rs.5. Show that 15 toys of type A and 30 of type B should be manufactured in a day to get maximum profit.

Every gram of wheat provides 0.1 g of proteins and 0.25 g of carbohydrates. The corresponding values of rice are 0.05 g and 0.5 g respectively. Wheat cost Rs.4 per kg and rice cost Rs.6 per kg. The minimum daily requirements of proteins and carbohydrate for an average child are 50 g and 200 g respectively. In what quantities should wheat and rice be mixed in the daily diet to provide minimum daily requirements of proteins and carbohydrate at minimum cost. Frame an LPP and solve it graphically.