C-Town brewery brews two beers: Expansion Draft and Burning River. Expansion Dra

Question

C-Town brewery brews two beers: Expansion Draft and Burning River. Expansion Draft sells for $20 a barrel, while Burning river sells for $8 a barrel. Producing a barrel of Expansion Draft requires 8 pounds of corn, and 4 pounds of hops. Producing a barrel of Burning River requires 2 pounds of corn, 6 pounds of rice, and 3 pounds of hops. The brewery has 500 pounds of corn, 300 pounds of rice, and 400 pounds of hops. Assuming a linear relationship, determine the optimal mix of Expansion Draft and Burning River that maximizes C-Town Brewery revenue.

Explanation / Answer

I put equal signs, because you want it to use as much of the brewery as possible.

500 = 8E + 2B
300 = 6B
400 = 4E + 3B
20E + 8B = revenue

Using the limitations on rice, B<=50.

Thus:

400 <= 8E for corn
350 <= 4E for hops

E >= 50

To find the maximum for E, assume B=0.

500 <= 8E
125 <= 2E
E <= 62.5 ~ 62 since you can't have half a barrel

If you plug in the maximums for E and B, you find the last equation is useless information as you can never run out.

250 = 4E + B from the first equation on corn
B = 250 - 4E

Use substitution:

20E + 8(250-4E) = f(x)
2000 - 12E = f(x)

To maximize f(x), you want to minimize E which was found to be 50.

2000 - 12(50) = 1400

With E and B as 50.

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.