Solve the below:
Q1) The total cost of producing x radio sets per day is $ ( 1/4 x^2 + 35x + 25 ) and the price per set is at which they may be sold is $ ( 50 - 1/2x ). Find the daily output for maximum profit.
Q2). The cost of fuel in running a locomotive is proportional to the square of the speed and is $25/hr for a speed of 25km/hr. The other costs are $100 /hr regardless of speed. Find the speed that will make the cost per kilometer a minimum.
Q2) A rectangular field , to enclose a given area , is fenced off along a straight river. If no fencing is needed along the river , show that the least amount of fencing will be required when the length of the field is twice the width ( this is all the info available- the condition ? length =2x width).