and
is to be divided into 3 rectangular rooms of equal size. The walls,
internal and external, will cost $60 per metre to build. What
dimensions should the shed have to minimize the cost of the walls?4.7 Optimization
In problem solving, the extreme values of a curve are sometimes called the optimum values. Sometimes we want to minimize cost or time, other times we want to maximize distance or volume.
Ex 1
An industrial shed is to have a total floor space of 600and
is to be divided into 3 rectangular rooms of equal size. The walls,
internal and external, will cost $60 per metre to build. What
dimensions should the shed have to minimize the cost of the walls?
Ex 2 Two numbers have a sum of 10. What is the maximum value of their product?
Ex 3 Find the most economical shape for a box with a square base, vertical sides and an open top, given that it must contain 4 litres.
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