In the statement below, the two blanks can be filled by positive single-digit numbers in such a way that the statement is always
1 answer:
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Answer:
Oatmeal cookies = 1 dozen
Sugar cookies = 7 dozen
Explanation:
Objective function:
Maximize: P = 3x + 2y
where
x = oatmeal cookies
y = sugar cookies
Constraints:
Since it takes 2 and 4 cups for oatmeal and sugar cookies respectively, and she has total 40 cups of sugar:
1) 3x+4y ≤ 40
The same for eggs:
2) 2x+y ≤ 20
She can make no more than 1 dozen oatmeal and 7 dozen sugar cookies:
3) x ≤ 1
4) y ≤ 7
Now graph these above four constraints equation( see the image below)
Now the corner points are :
(0,7), (1,7), (1,0), (0,0)
Put these corner points in objective function:
for (0,7) : P = ( 3×0 ) + ( 2×7 ) = 14
for (1,7) : P = ( 3×1 ) + ( 2×7 ) = 17
for (1,0) : P = ( 3×1 ) + ( 2×0 ) = 3
for (0,0) : P = ( 3×0 ) + ( 2×0 ) = 0
Since the maximum profit = 17 comes from the point (1,7), she should make 1 dozen of oatmeal cookies and 7 dozen of sugar cookies.
