Below is the question and I have already answered #$1.$ I need help with #$2.$ Details on how you got to the answer is very helpful. CNY Electronics operates production for two kinds of audio speakers. The first kind is a bookshelf speaker, called Utopia. The other kind is a floor speaker, called Vienna. Due to Vienna$$s high shipping cost and heavy weight, only a small portion of consumers will consider Vienna. Thus, CNY Electronics wants Vienna$$s monthly production to be no more than $200$ units.

In the production line, each Utopia requires $1$ tweeter and $2$ woofers to produce sound while each Vienna requires $2$ tweeters and $3$ woofers to do so$.$ There are $800$ tweeters and $1500$ woofers available monthly from CNY Electronics$$ suppliers.

In order to maintain its work force contract, at least $500$ audio speakers or more must be produced monthly. Currently each Utopia can bring in $$500$ as its unit profit and each Vienna can bring in $$1250$ as its unit profit. CNY Electronics wants to find a production mix for Utopia and Vienna to maximize its monthly profit.

$1)$ Formulate this problem as a linear program.

The variables:

X$=$ Utopia bookshelf speakers produced per month

Y$=$ Vienna floor speakers produced per month

The objective function:

We would want to maximize the monthly profit with Z$.$

Z$=500($X$)+1250($Y$)$

Constraints:

The Vienna production should be no more than $200$ units. Y $<=200$

Utopia requires $1$ tweeter and Vienna requires $2$ tweeters. X$+2$Y$<=800$

Utopia requires $2$ woofers and Vienna requires $3$ woofers. $2$X$+2$Y$<=1500$

At least $500$ audio speakers must be produced monthly. X$+$Y$>=500$

$2)$ Use the graphical solution procedure to solve this linear program graphically for its optimal solution. Report the optimal solution.