An ice cream store has two new flavors: Fantasy and Ecstasy. Each barrel of Fantasy requires 4
1 answer:
Answer:
- Fantasy: 3 barrels
- Ecstasy: 1 barrel
Step-by-step explanation:
<u>Given</u>
Fantasy uses 4 lb of nuts, 3 lb of chocolate, for a profit of $50
Ecstasy uses 4 lb of nuts, 1 lb of chocolate, for a profit of $40
In stock are 16 lb of nuts, 10 lb of chocolate
<u>Find</u>
amount of each to maximize profit
<u>Solution</u>
Let x and y represent barrels of Fantasy and Ecstasy, respectively. Then the limitations on production are ...
4x +4y ≤ 16 . . . lb of nuts
3x +y ≤ 10 . . . . lb of chocolate
We want to maximize
50x +40y
The graph shows the feasible region. Its vertices are ...
(0, 4), (3, 1), (3.33, 0)
Profit is maximized at $190 when production is 3 barrels of Fantasy and 1 barrel of Ecstasy.
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Answer:
A. $301
B. $721
Step-by-step explanation:
Let $x be the amount of money they raised.
Rowena tried to put the $1 bills into two equal piles and found one left over at the end, then
Polly tried to put the $1 bills into three equal piles and found one left over at the end, then
Frustrated, they tried 4, 5, and 6 equal piles and each time had $1 left over, then
Finally Rowena put all the bills evenly into 7 equal piles, and none were left over, then
This means is divisible by 2, 3, 4, 5 and 6 without remainder, so
Hence,
The smallest amount of money they could have raised is $301, because
is divisible by 7.
Now, the number should be divisible by 7 and must be greater than 500.
So,
When n = 9,
is not divisible by 7.
When n = 10,
is not divisible by 7.
When n = 11,
is not divisible by 7.
When n = 12,
is divisible by 7.
B. The least amount of money they could have raised is $721