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A taxi company has “SUPER” taxis and “MINI” taxis. One morning a group of 45 people needs taxis.

For this group the taxi company uses x “SUPER” taxis and y “MINI” taxis.

A “SUPER” taxi can carry 5 passengers and a “MINI” taxi can carry 3 passengers.

So 5x + 3y 45.

(a) The taxi company has 12 taxis.

Write down another inequality in x and y to show this information.

(b) The taxi company always uses at least 4 “MINI” taxis.

Write down an inequality in y to show this information.

(c) Draw x and y axes from 0 to 15 using 1 cm to represent 1 unit on each axis.

(d) Draw three lines on your graph to show the inequality 5x + 3y 45 and the inequalities from parts

(a) and (b).

Shade the unwanted regions. [6]

(e) The cost to the taxi company of using a “SUPER” taxi is $20 and the cost of using a “MINI” taxi is

$10.

The taxi company wants to find the cheapest way of providing “SUPER” and “MINI” taxis for this

group of people.

Find the two ways in which this can be done.

(f) The taxi company decides to use 11 taxis for this group.

(i) The taxi company charges $30 for the use of each “SUPER” taxi and $16 for the use of each

“MINI” taxi.

Find the two possible total charges.

(ii) Find the largest possible profit the company can make, using 11 taxis. 22.03.2015

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by shyxaa

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