NZ Level 8 (NZC) Level 3 (NCEA) [In development]

Linear Programming - Objective Function

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

The square boxes cost $\$55$$55 each and have a volume of $2$2 m^{3} and the rectangular boxes cost $\$65$$65 each and have a volume of $7$7 m^{3}. The warehouse has a total storage space of $200$200 m^{3} and there is a budget of $\$800$$800 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

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Use curve fitting, log modelling, and linear programming techniques

Apply linear programming methods in solving problems