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Answer:
He should prepare 260 pounds of first mixture and 0 pounds of second mixture
Step-by-step explanation:
Let x be the total quantity ( in pounds ) of cherries and mints in the first mixture and y be the total quantity in second mixture,
Since, first mixture will contain half cherries and half mints by weight,
That is, in first mixture,
Cherries =
Mints = ,
While, second mixture will contain one-third cherries and two-thirds mints by weight,
That is, in second mixture,
Cherries =
Mints =
According to the question,
The manufacturer has 130 pounds of chocolate-covered cherries and 170 pounds of chocolate-covered mints in stock,
That is,
Also, pounds can not be negative,
x ≥ 0, y ≥ 0,
Since, the first and second mixture must be sell at the rate of $2.00 per pound and $1.25 per pound respectively,
Hence, the total revenue,
Z = 2.00x + 1.25y
Which is the function that have to maximise,
By plotting the above inequalities,
Vertex of feasible regions are,
(0,255), (180, 120) and (260, 0),
Also, at (260, 0), Z is maximum,
Hence, he should prepare 260 pounds of first mixture and 0 pounds of second mixture in order to maximize his sales revenue.
