Answer:
For the first one
Part a:
115x + 685y >= 2300
Part b:
See explanation below
Second one:
1.5x + 1.0y >= 2000
Rest of explanation below
Explanation:
First one.
Let x be the number of skimboards sold and y be the number of longboards sold.
Then revenue from sales of x units at $115 and y units at $685 would be
115x + 685y
This must be at lest the overhead to make zero loss
So the inequality is
115x + 685y ≥ 2300 (Answer a)
Part b
Any combination of x and y which satisfies this inequality will provide a profit. I have provided a graph of this inequality using an online graphing calculator. I am not sure what your teacher wants you to use.
Any point in the shaded region represents a combination of x and y which satisfies that inequality. However since you cannot sell a fraction of a surfboard, only points which represent whole numbers can be valid. Also only values of x and y >=0 can be chosen. So any point in the shaded region which has x and y non-negative and x and y whole numbers will generate a profit
Again I am not sure whether this question is asking for a specific value or possible values.
A specific value can be (x=5, y = 10) which is well within the shaded region. This represents 5 skimboards and 10 longboards with a revenue of 5 x 115 + 10 x 685 = $ 7425
Or you could sell 0 skimboards and 4 longboards giving you a revenue of
4 x 685 = $2,740
Or 20 skimboards and zero long boards which is a revenue of $2300 which breaks even with the overhead
Second Question: Modeling
Using x for number of hot dogs sold and y for number of sodas, the inequality is
(a) 1.0x + 1.25y >= 2000
(b) Graph attached
(c) 5 solution points plotted
Here are 5 values that fill fit the inequality
- 1000 hot dogs, 1000 sodas (Point A)
- 400 hot dogs, 1400 sodas (Point B)
- 600 hot dogs, 1200 sodas (Point C)
- 0 hot dogs, 1800 sodas (Point D)
- 1600 hot dogs, 800 sodas (Point E)
Hope that helps. Sorry, best I could do