Question

Customers buy 14 units of regular beer and 15 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 $30,000 and the cost per unit of light beer is $48,000. Every unit of regular beer brings in $250,000 in revenue, while every unit of light beer brings in $500,000 in revenue. The brewery wants at least $20,000,000 in revenue. At least 31 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=___y_(1)+___y_(2)

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

What is the minimum cost?

The minimum cost is $___

(b) Suppose the minimum revenue is increased to $20,400,000. Use shadow costs to calculate the new total production costs.

$____

Answer 1