A fruit juice manufacturer wishes to design a carton that has a square face, as shown in Figure 8.17(a). The carton is to contain 1 litre of juice and is made from a rectangular sheet of waxed cardboard by folding it into a rectangular tube and sealing down the edge and then folding and sealing the top and bottom. To make the carton airtight and robust for handling, an overlap of at least 0.5 cm is needed. The net for the carton is shown in Figure 8.17(b). Show that the amount A(h) cm² of card used is given by

By finding the value x* of x which minimizes

find the value h* of h which minimizes A(h).

Transcribed Image Text:

A(h) = h + Verify that 1000 h A(h) = 2 h + + 1 2h+ 1 1000 h + N 5 31- 8 2000 h 9 32 +0.5