A milk carton has capacity 2 pints (1136 ml) It is made from a rectangular waxed card using the net shown in Figure 1 37 Show that the total area A (mm 2 ) of card used is given by A(h, w) (2w 145)(h 80) with hw 113 600 7 Show that with equality when 160w 145h Hence show that the minimum values of ...

Area of card 4hw w 70w70w5535h355 2w 145h80 Capacity is hxwx 70 and equals 113 ...

A milk carton has capacity 2 pints (1136 ml). It is made from a rectangular waxed card

Question:

A milk carton has capacity 2 pints (1136 ml).

It is made from a rectangular waxed card using the net shown in Figure 1.37. Show that the total area A (mm²) of card used is given by A(h, w) = (2w + 145)(h + 80)

with hw = 113 600/7. Show that

A(h, w) = C(h, w) + 308 400 7 where C(h, w) = 145h + 160w. Use the arithmetic-geometric inequality to show

with equality when 160w = 145h. Hence show that the minimum values of C(h, w) and A(h, w) are achieved when h = 133.8 and w = 121.3.
Give these answers to more sensible accuracy.

Figure 1.37

hmm 70 mm Semi- skimmed milk 2 pint W mm mm > 70 mm > 35 mm < w mm > 35 mm <70 mm 5 mm overlap 5 mm overlap