>>>.....determine the blend mix that will meet
customer requirements and maximize profits.
Let x = the gallons of blend that will meet customer requirements.
The distillery can produce (no more than) 500 gallons per week, regardless
of the blend.
x ≤ 500
the blend should be mixed in the ratio of two parts rye to one part bourbon.
gallons of rye = (2/3)x
gallons of bourbon = (1/3)x
the order must contain at least 40 percent rye
This requirement is automatically fulfilled by the above because 2/3 is
about 66.7% which is more than 40%, and is certainly "at least 40%."
the order must contain.....not more than 250 gallons of bourbon.
(1/3)x ≤ 250
x ≤ 750
This requirement is automatically fulfilled because x ≤ 500
The blend is sold for $12 per gallon. The distillery company’s cost per
gallon is $4 for rye and $2 for bourbon.
Profit = 12x - 4(2/3x) - 2(1/3x) = (26/3)x
Since (26/3)x is a increasing function, since its slope 26/3 is positive,
so the maximum profit will be greatest when x is greatest, which is when
x = 500, so we substitute:
Maximum profit = (26/3)(500) = $4333.33 when there is 500 gallons of custom-
blended whiskey.
Edwin
