A 15,000 litre rainwater tank is to be built in the shape of a cylinder. It must be at most 3 metres tall, and have radius at most 2 metres. Its base costs 40 dollars per square metre, and the sides and top cost 20 per square metre. What are the cheapest and most expensive shapes that satisfy these conditions?

a)Give the total cost as a function of the heightHand radiusR.Use units of metres for bothHandR.Note that it is case sensitive - you must use exactly the variable names given in the question.

b)Give an equation that connects the heightHand radiusR.Your answer must be an equation including =. Remember to use consistent units.

c)Write the cost as a function just ofR.

d)For which value ofRdoes this cost function have a local minimum? Enter in metres, accurate within a centimetre.

e)What is the smallest allowed radiusR,that keeps the height within bounds? Answer as a decimal in metres, accurate within a centimetre

f)What is the largest allowed radiusR?

g) Enter the cheapest cost, accurate to within a dollar