Customers buy $11$ units of regular beer and $16$ units of light beer monthly. The brewery decides to produce extra beer,

beyond that needed to satisfy the customers. The cost per unit of regular beer is $$28,000$ and the cost per unit of light

beer is $$40,000.$ Every unit of regular beer brings in $$100,000$ in revenue, while every unit of light beer brings in

$$200,000$ in revenue. The brewery wants at least $$6,000,000$ in revenue. At least $20$ additional units of beer can be sold.

Complete parts $($a$)$ and $($b$).$

$($a$)$ How much of each type of beer should be made so as to minimize total production costs?

Let $y_1$ represent units of regular beer and $y_2$ represent units of light beer. Find the objective function, $w,$ used to

minimize production costs.

$w=28000y_1+40000y_2$

$($Do not include the $ symbol in your answers.$)$

The brewery should make units of regular beer and units of light beer so as to minimize total production costs.