The Aviston Electronics Company manufactures motors for toys and small appliances. The

marketing department is predicting sales of $6,100$ units of the Dynamonster motor in the next

quarter. This is a new high and meeting this demand will test Aviston's production capacities.

A Dynamonster is assembled from three components: a shaft, base, and cage. It is clear that

some of these components will have to be purchased from outside suppliers because of

limited in$-$house capacity. The variable in$-$house production cost per unit is compared with the

outside purchase cost in the following table:

Aviston's plant consists of three departments. The time requirements in hours of each

component

in each department if manufactured in$-$house are summarized in the following table. The

hours available for Dynamonster production are listed in the last row:

Develop a LINGO model using SETS and DATA to answer the following questions:

How many decision variables are in the model?

Which, if any, departments have slack capacity?

What is the maximum price Aviston would pay to purchase an additional hour of time in the

Shapting Department? $($round your answer to $2$ decimals, no $$-$sign or comma$)$:

In the optimum solution there was one component that was not purchased from outside.

Which component was it$,$ and what would the cost of that component need to be in order for

Aviston to consider purchasing it$?($round your answer to $2$ decimals, no $$-$sign or commas$)$: