Max/ Min Optimization problem set

The following is a 25 mark test, this cover max/ min optimization problems – this should take 45 mins under exam conditions.


1a) Two circles radii sum to 100 m. One circle has radius x m, show the area of both circles is represented by the equation below:

A = 2(x2 – 100x + 5000)[2 marks]

b) For what value of x do these circles have the smallest area? [2 marks]

2) A soft drink company is designing their aluminium cans and want to optimize the greatest volume for the aluminium sheet of 200 cm2. What is the maximum volume this can be? [4 marks]

3) A rectangular prism shaped room for a house is being built, however, the painter wants the room to have every edge painted with paint. What dimensions of the 300 mroom will minimize the amount of paint that must be applied to all of the edges. [5 marks]

From past HSC Questions:

2013 HSC Q14 B

2014 HSC Q 16C


1b) x = 50 cm

2) r = 103h = 11.5

3) x = 7.3 m, y = 3.6 m and z = 11.4 m


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