Course Objectives

$2\mathrm{.}2\mathrm{.}8$ Graph a quadratic function, finding its vertex and intercepts.

$2\mathrm{.}2\mathrm{.}11$ Solve application problems involving functions.

$2\mathrm{.}2\mathrm{.}12$ Build mathematical models that involve functions.

Maximizing Shipping Volume

Operations Management

In a business, operations management is concerned with all of the functions that are involved in the

process of creating and distributing the company's products or services. In a distribution company like

Amazon, for example, operations means making sure orders are processed on time, product is packaged

and shipped properly and returns are properly entered and credited to the customer. Amazon does this

using a fleet of automated robots ${?}^1$ and complex software that tracks their movements and the location

of every object in the warehouse. Operations managers and analysts are responsible for designing and

maintaining systems like this that maximize the effectiveness of an operation.

When managing the shipping process, operations analysts work to minimize a company's shipping costs

by choosing the proper packaging size, negotiating terms with transport companies like UPS and FedEx

and following the shipping policies of those companies. In the following scenario, you'll assume the role

of an operations analyst who has to determine the best possible size of a shipping container based on

UPS's size limitations$.$

The Scenario

UPS defines the size of a box to be equal to its length plus twice its width plus

twice its height:

size $=$ length $+2*$ width $+2*$ height

In order to avoid being charged freight charges, the size of a package has to be

less than or equal to ${165}^{\text{'}\text{'}}$ and the length has to be less than ${108}^{\text{'}\text{'}}.{?}^2$

You work for a wine producer who ships wine bottles in rectangular boxes that are ${13}^{\text{'}\text{'}}{4}^{\text{'}\text{'}}{4}^{\text{'}\text{'}}.$ The

individual boxes are packaged into larger rectangular boxes for shipping. In order to go through the

company's production line, the length of the boxes has to be ${13}^{\text{'}\text{'}}.$