Customers buy 14 units of regular beer and 20 units of light beer monthly. The b

Question

Customers buy 14 units of regular beer and 20 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 $33,000 and the cost per unit of light beer is $44,000. Every unit of regular beer brings in $200,000 in revenue, while every unit of light beer brings in $400,000 in revenue. The brewery wants at least $16,000,000 in revenue. At least 18 additional units of beer can be sold. How much of each beer type should be made so as to minimize total production costs? What is the minimum cost?

Explanation / Answer

It seems like showing that it has exactly 12 pentagons follows easily after you show that it must have at least 12 pentagonal faces. For example, say you have p pentagonal faces and h hexagonal faces, then there are p+h faces, so p+h=f Also if e = # of edges, then 5p+6h=2e (5p counts the edges of each pentagonal face, 6h counts the edges of each hexagonal face, and it equals 2e because you have counted each edge twice) Now using the inequality from this question:

It seems like showing that it has exactly 12 pentagons follows easily after you show that it must have at least 12 pentagonal faces. For example, say you have p pentagonal faces and h hexagonal faces, then there are p+h faces, so p+h=f Also if e = # of edges, then 5p+6h=2e (5p counts the edges of each pentagonal face, 6h counts the edges of each hexagonal face, and it equals 2e because you have counted each edge twice) Now using the inequality from this question:

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