Answers to all pages - Hodder Plus Home
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Model answers<br />
Linear programming (page 41)<br />
1 (a) Type A takes 1 hour of machine time and type B takes 2 hours. There are 28 hours of<br />
machine time in a day.<br />
x + 2y 28<br />
Type A takes 3 hours of workers’ time and type B takes 1 hour. There are 24 hours of workers’<br />
time in a day.<br />
3x + y 24<br />
(b) y<br />
30<br />
24<br />
20<br />
14<br />
10<br />
O<br />
3x + y = 24 x + 2y = 28<br />
8 28 x<br />
10 20<br />
30<br />
(c) (i) The greatest profit will result from either the greatest number of type A, the greatest number of type<br />
B or the greatest <strong>to</strong>tal number of items so test the points (8, 0), (0, 14) and (4, 12).<br />
Profit at (8, 0) = $160.<br />
Profit at (0, 14) = $140.<br />
Profit at (4, 12) = $80 + $120 = $200.<br />
So the greatest profit that can be made is $200.<br />
(ii) 4 type A and 12 type B.<br />
2 (a) (i) There is $1000 available; paperback books cost $10 and hardback books cost $25.<br />
So 10x + 25y 1000.<br />
Dividing by 5 gives 2x + 5y 200.<br />
(ii) y > x and x + y 50<br />
(b) y<br />
50<br />
y = x<br />
40<br />
20<br />
O<br />
(c) 33 hardback books<br />
50<br />
x + y = 50<br />
x<br />
100<br />
2x + 5y = 200<br />
IGCSE Revision Guide for Mathematics Model <strong>Answers</strong> © 2004, <strong>Hodder</strong> & S<strong>to</strong>ugh<strong>to</strong>n Educational<br />
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