Homework Help: Math

Posted by Mike on Tuesday, November 29, 2011 at 1:20am.

You own a small winery that produces two types of Chardonnay, an extra extra oaky one and an oaky one. The wines are produced from the same grapes. Furthermore, both wines are aged in oak barrels, and have additional oak chips added into the oak barrels. However, the extra extra oaky one requires twice as many added oak chips as the oaky one. The extra extra oaky Chardonnay has a profit of $15 per bottle, and the oaky Chardonnay has a profit of $10 per bottle. You have enough grapes to make a total of 500 bottles of Chardonnay (regardless of if the type is extra extra oaky or oaky), and enough oak chips to make a total of 800 bottles of oaky Chardonnay. How many bottles of oaky Chardonnay should you produce?

Math - Reiny, Tuesday, November 29, 2011 at 8:10am
let number of oaky bottles be x
let number of extra oaky bottles be y

x+y ≤ 500 based on grapes
2x + y ≤ 800 based on chips

graph both lines and consider the region bounded by the x-axis, the y-axis and the two boundary lines
It can be easily found that the two boundary lines intersect at (300,200)
Also considering the intercepts, the "corners" of the region are
(0,0), (0,250), (300,200) and (400,0)

The profit equation would be
P = 10x + 15y
for (300,200), P = 3000 + 3000 = 6000
for (0,250) , P = 0 + 3750
for (400,0) , P = 4000 + 0 = 4000

They should produce 300 bottles of oaky, and 200 of the extra oaky.

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