Question 14:
A factory produces premium handbags and exclusive handbags. The weekly production targets are as follows:
(a) Using x to represent the number of premium handbags and y to represent the number of exclusive handbags, write two linear inequalities, other than x ≥ 0 and y ≥ 0, to represent the situation.
[2 marks]
(b)(i) The third weekly production target is shown by the shaded region on the graph in the answer space on page 161. Write in words the inequality that represent the target.
[1 mark]
(ii) Hence on the same graph, draw and shade the region that satisfies the system of linear inequalities in (a), (b)(i) and x ≥ 0, y ≥ 0.
[3 marks]
(c) From the graph in (b), determine
(i) the maximum number of exclusive handbags that can be produced,
[1 mark]
(ii) whether the weekly production targets are achieved if 25 premium handbags and 60 exclusive handbags are produced in a particular week.
Justify your answer.
[2 marks]
Answer:
Answer:
(a) x ≤ 42
y ≤ 2x
(b)(i)
The number of exclusive handbags produced is greater than 46.
(b)(ii)
(c)(i)
The maximum number of exclusive handbags = 83
(c)(ii)
No.
Point (25, 60) locates outside of the shaded region.
A factory produces premium handbags and exclusive handbags. The weekly production targets are as follows:
| – The maximum number of premium handbags produced is 42 . – The number of exclusive handbags produced is at most two times the number of premium handbags produced. |
[2 marks]
(b)(i) The third weekly production target is shown by the shaded region on the graph in the answer space on page 161. Write in words the inequality that represent the target.
[1 mark]
(ii) Hence on the same graph, draw and shade the region that satisfies the system of linear inequalities in (a), (b)(i) and x ≥ 0, y ≥ 0.
[3 marks]
(c) From the graph in (b), determine
(i) the maximum number of exclusive handbags that can be produced,
[1 mark]
(ii) whether the weekly production targets are achieved if 25 premium handbags and 60 exclusive handbags are produced in a particular week.
Justify your answer.
[2 marks]
Answer:
Answer:
(a) x ≤ 42
y ≤ 2x
(b)(i)
The number of exclusive handbags produced is greater than 46.
(b)(ii)
(c)(i)
The maximum number of exclusive handbags = 83
(c)(ii)
No.
Point (25, 60) locates outside of the shaded region.