The Electrocomp Corporation manufactures two electrical products: air conditioners and large fans. The assembly process for each is similar in that both require a certain amount of wiring and drilling. Each air conditioner takes $3$ hours of wiring and $2$ hours of drilling. Each fan must go through $2$ hours of wiring and $1$ hour of drilling. During the next production period, $240$ hours of wiring time are available and up to $140$ hours of drilling time may be used. Each air conditioner sold yields a profit of $$25.$ Each fan assembled may be sold for a $$15$ profit. Formulate and solve this LP production$-$mix situation, and find the best combination of air conditioners and fans that yields the highest profit. $--$

Solve it with this outlineStep by Step $-$ LP Solution Outline

Step $1$: Construct a Data Table & Designate the Variable Expressions

Step $2$: Identify the Objective Function & the Constraint Functions

Objective Function

Maximize Profit:

Minimize Cost:

Subject to the following constraints $($name each$)$:

Constraint:

Constraint:

Constraint:

Non$-$Negativity Constraint:

Step $3$: Find the Sets of Coordinates $($X$,$ Y$)$ for the Constraints

Step $5$: Corner Point Method

Identify the extreme points from Step $4.$ Keep in mind the non$-$negativity constraint.

Step $6$: Simultaneous Equations Method

Point

Point

Point

Step $7$: Optimal Solution & Profit Summary

$x=$

Profit $\frac{?}{?}$ Cost $=$$