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

A bakery owner makes two types of cakes A and B.There machines are needed for this purpose.The time(in minutes) required for making each type of cakes in each machine is given below, Each machine is available for atmost 6 hours per day.Assume that all cakes will be sold out everyday.The bakery owner wants to make maximum profit per day by making Rs.7.5 from type A and Rs.5 from type B. Find the maximum profit graphically.

A magnetic field of 100 G (1 G = 10^(-4)T) is required which is uniform in a region of linear dimension about 10 cm and area of cross-section about 10^(-3) m^(2) . The maximum current carrying capacity of a given coil of wire is 15A and the number of turns per unit length that can be wound round a core is at most 1000 turns m^(-1). Suggest some appropriate design particulars of a solenoid for the required purpose. Assume the core is not ferromagentic.