$($Note: Adapted from Winston$/$Albright$)$ Easy Rider Toys $($ERT$)$ manufactures and markets toy cars. This

year ERT is planning to introduce several new product lines and wants to sell off existing inventories.

These inventories consist of toy cars and toy trucks and can be sold in two different sets.

$$ The Racer Set consists of seven cars and two trucks and $3$ spare tires and is sold for $$34\mathrm{.}99.$

$$ The Construction Set consists of three cars and twelve trucks and $6$ spare tires and is sold for

$$43\mathrm{.}99.$

$$ The NASCAR set consists of $1$ car, $1$ truck, $8$ spare tires, and sells for $$5\mathrm{.}99.$

Currently there are $10,000$ cars and $12,000$ trucks and $10,000$ spare tires in inventory.

ERT must manufacture at least $700$ construction sets due to a contractual obligation with Zamazon.com.

$8$

ERT figures that it cannot sell more than $1,000$ units of the Racer Set or more than $1,000$ units of the

Construction Set and can$$t sell more than $300$ of the NASCAR set. This is from Divya in the Marketing

Department, and reflects her prediction of the number of customers; ERT shouldn$$t build more sets than

it can sell.

Tallulah, the COO, has enlisted your help to optimize which sets to assemble in order to maximize profit.

Build the optimization model from scratch that maximizes revenue. $($Don$$t make any integer

constraints$)$

Hints:

$$ This has similar elements to Legos

$$ If you build $10$ sets of each, you should have sales of about $$850($although this far from

validates your model, it is a start$)$

Answer the following questions:

A$)$ What are the three parts of the optimization problem?

$1.$ The objective

$2.$ The decision variables

$3.$ The constraints

B$)$ What dimension is the corresponding polygon?

C$)$ A binding constraint is one in which the inequality is satisfied by equality $($i$.$e$.,5<=5$ is a binding

constraint, whereas $3<=6$ is not a binding constraint$).$ Binding constraints are those that might

$$matter$$ and affect the shape of our polygon and as such might have an effect on our optimal

solution. For instance, in the Legos example, labor was not a binding constraint, but small

blocks and large blocks available were both binding constraints, b$/$c changing each by even a

little affected our optimal solution. Which of the constraints are binding?

D$)$ Of what value $($in dollars$)$ would it be to do the following:

$1.$ Build $10$ more cars to have available for the sets?

$2.$ Build $10$ more trucks to have available for the sets?

$9$

$3.$ Reduce the tires included in the NASCAR pack from $8$ to $7?$

$4.$ Work with your marketing department to advertise and increase demand for the Racers

set by $10\%($change tires included back to $8)?$

$5.$ Work with your marketing department to increase demand for the NASCAR set by $10\%?$

$6.$ Renegotiate your contract with Zamazon.com?

E$)$ Paste your model to an Excel tab.