Jenna eats dinner at a restaurant. Her bill is $14.50 Jenna pays her bill and leaves a tip. Write an inequality to represent the
1 answer:
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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.
Inequation 1:
to plot the pairs (x, y) for which the inequation holds, draw the line
then pick a point in either side of the line. If that point is a solution of the inequation, than color that region of the line, if that point is not a solution, then color the other part of the line.
we do the same for the second inequation. Then the solution, is the region of the x-y axes colored in both cases.
inequation 2:
draw the lines
i) use points (0, -3), (3, -1)
ii)
use points ( 0, 4), (3, 2)
let's use the point P(3, 3) to see what region of the lines need to be coloured:
;
, not true so we color the region not containing this point
not true, so we color the region not containing the point (3, 3)
The graph representing the system of inequalities is the region colored both red and blue, with the blue line not dashed, and the red line dashed.
to plot the pairs (x, y) for which the inequation holds, draw the line
then pick a point in either side of the line. If that point is a solution of the inequation, than color that region of the line, if that point is not a solution, then color the other part of the line.
we do the same for the second inequation. Then the solution, is the region of the x-y axes colored in both cases.
inequation 2:
draw the lines
i)
ii)
let's use the point P(3, 3) to see what region of the lines need to be coloured:
The graph representing the system of inequalities is the region colored both red and blue, with the blue line not dashed, and the red line dashed.