 Hong Kong
Stage 4 - Stage 5

# Linear Programming - Constraints and Objectives

## Interactive practice questions

A warehouse is stocked with two types of storage containers: square boxes and rectangular boxes.

The square boxes cost $\$55$$55 each and have a volume of 22 m3 and the rectangular boxes cost \65$$65 each and have a volume of $7$7 m3. The warehouse has a total storage space of $200$200 m3 and there is a budget of $\$800800 to purchase the containers.

a

Let $x$x represent the number of square boxes purchased, and $y$y represent the number of rectangular boxes purchased.

Fill in the gaps to complete the following constraint inequalities for $x$x and $y$y:

$x\ge\editable{}$x

$y\ge\editable{}$y

b

Write an inequality relating $x$x and $y$y to the total budget for the warehouse:

c

Finally, write an inequality relating $x$x and $y$y to the total storage space of the warehouse:

Easy
Approx 4 minutes

A light bulb manufacturer produces two types of light bulbs, incandescent and fluorescent.

We can let $x$x represent the number of incandescent bulbs produced in a day, and $y$y represent the number of fluorescent bulbs produced in a day.

Up to $200$200 light bulbs can be produced in one day.

A company produces cans of cat food and dog food. Each product passes through two machines in their production, and the amount of time each machine takes to process one pallet of pet food is shown in the table below. Each machine can operate for 12 hours in a day.

Let $x$x represent the number of pallets of cat food processed each day, and $y$y represent the number of pallets of dog food processed each day.