Soalan 15:
Club staff SMK Sri Pinang wants to organise a Family Day. They plan to order same type of t-shirt for adults and children. They order x pieces of adult t-shirts and y pieces of children’s t-shirts. The order of t-shirts is based on the following constraints:
I The total number of both t-shirts is at most 80 pieces.
II The total number of children’s t-shirts is at most double of the adult’s t-shirts.
III The minimum number of children’s t-shirts ordered is 10 pieces.
(a) Based on the given information, write three linear inequalities other than x ≥ 0 and y ≥ 0. [3 marks]
(b) For this part of the question, use the graph paper provided on page 31.
Using the scale of 2 cm to 10 pieces of t-shirts on both axes, draw and shade the region that satisfies the system of linear inequalities in 15(a). [4 marks]
(c) Based on the graph in 15(b),
(i) determine the maximum number of children’s t-shirts if 70 adults’ t-shirts are purchased. [1 mark]
(ii) calculate the amount of maximum payment if the price of an adult t-shirt and a child t-shirt is RM35 and RM20 respectively. [2 marks]
Penyelesaian:
(a)
– The total number of both t-shirts is at most 80 pieces, x + y ⩽ 80.
– The total number of children’s t-shirts is at most double of the adult’s t-shirts, thus, y ⩽ 2x.
– The minimum number of children’s t-shirts ordered is 10 pieces, y ⩾ 10.
(c)
(c)(i)
From the graph, if 70 adults’ t-shirts are purchased, the maximum number of children’s t-shirt is 10 pieces.
(c)(ii)
Maximum payment
= 35(70) + 20(10)
= RM2650
Club staff SMK Sri Pinang wants to organise a Family Day. They plan to order same type of t-shirt for adults and children. They order x pieces of adult t-shirts and y pieces of children’s t-shirts. The order of t-shirts is based on the following constraints:
I The total number of both t-shirts is at most 80 pieces.
II The total number of children’s t-shirts is at most double of the adult’s t-shirts.
III The minimum number of children’s t-shirts ordered is 10 pieces.
(a) Based on the given information, write three linear inequalities other than x ≥ 0 and y ≥ 0. [3 marks]
(b) For this part of the question, use the graph paper provided on page 31.
Using the scale of 2 cm to 10 pieces of t-shirts on both axes, draw and shade the region that satisfies the system of linear inequalities in 15(a). [4 marks]
(c) Based on the graph in 15(b),
(i) determine the maximum number of children’s t-shirts if 70 adults’ t-shirts are purchased. [1 mark]
(ii) calculate the amount of maximum payment if the price of an adult t-shirt and a child t-shirt is RM35 and RM20 respectively. [2 marks]
Penyelesaian:
(a)
– The total number of both t-shirts is at most 80 pieces, x + y ⩽ 80.
– The total number of children’s t-shirts is at most double of the adult’s t-shirts, thus, y ⩽ 2x.
– The minimum number of children’s t-shirts ordered is 10 pieces, y ⩾ 10.
(b)
x + y = 80
x + y ⩽ 80
y = 2x
y ⩽ 2x
y = 10
y ⩾ 10
(c)
(c)(i)
From the graph, if 70 adults’ t-shirts are purchased, the maximum number of children’s t-shirt is 10 pieces.
(c)(ii)
Maximum payment
= 35(70) + 20(10)
= RM2650