GRAPHS, FUR1 2002 VCAA 9 MC

A company uses both trainee and qualified inspectors for quality control on an assembly line. The trainee inspectors can examine `15` items per hour, while the qualified inspectors can examine `25` items per hour.
The company needs at least `1800` items inspected in each eight-hour day.
Let `x` be the number of trainee inspectors employed by the company, and `y` be the number of qualified inspectors employed.
The constraint imposed by the number of items that need to be inspected in an eight-hour day is expressed by the inequality

A. `8x + 8y ≥ 1800`

B. `15x + 25y ≤ 1800`

C. `15x + 25y ≥ 1800`

D. `120x + 200y ≥ 1800`

E. `120x + 200y ≤ 1800`

Show Answers Only

`D`

Show Worked Solution

`x = text(no. trainees)`

`y = text(no. qualified)`

`text(1 trainee inspects 15 items/hr)`

`text(1 qualified inspector inspects 25 items/hr)`

`text(Hence in 8 hrs)`

`text(No. items trainee inspects)`

`= 15x xx 8text(hrs)`

`= 120x`

`text(No. items qualified inspector inspects)`

`= 25y xx 8text(hrs)`

`= 200y`

`text(At least 1800 items inspected in 8 hrs.)`

`:.\ 120x + 200y ≥ 1800`

`=> D`