While traveling for vacation, you have decided to divide your lodging between a resort and a regular stay hotel. Let x represent the number of nights you will spend in a resort and let y represent the number of nights you will spend in a regular stay hotel.
A) Write a system of inequalities that models the following conditions:
1) You want to stay at least 5 nights
2) At least one night will be spent at a resort
3) Resorts average $200 per night and regular stay hotels average $100 per night. Your budget does not exceed $700 for lodging
B) How do I graph the solution set of my system of inequalities?
C) How many nights can you spend at resort and stay within your budget?
Please help!!!!! A-C step by step
google linear programming
for example
http://www.wolframalpha.com/widget/widgetPopup.jsp?p=v&id=1e692c6f72587b2cbd3e7be018fd8960&title=Linear%20Programming%20Calculator&theme=blue
Can you just do the step by steps to get to the answers please? I have the answers with me, but want to double check the work and answers please!!!!!!
on axis system draw x = 1 vertical line, must be to right
draw y = 5-x
must be to right , intersect at (1,4)
draw y = 7 -2 x must be to left
(this is from 200 x100 y <=700)
that hits x = 1 at y = 5
it hits y = 5-x at
7-2x = 5-x
x = 2
That is the biggest x that works
A) To write a system of inequalities that models the given conditions, we can break down the conditions into individual inequalities.
1) You want to stay at least 5 nights:
x + y ≥ 5
2) At least one night will be spent at a resort:
x ≥ 1
3) Your budget does not exceed $700 for lodging:
200x + 100y ≤ 700
Therefore, the system of inequalities is:
x + y ≥ 5
x ≥ 1
200x + 100y ≤ 700
B) To graph the solution set of the system of inequalities, we need to start by graphing each individual inequality on the same coordinate plane.
First, let's graph the inequality x + y ≥ 5:
1) Draw a line with a slope of -1 passing through the point (0, 5).
2) Shade the region above the line to represent x + y ≥ 5.
Next, let's graph the inequality x ≥ 1:
1) Draw a vertical line passing through the point (1, 0).
2) Shade the region to the right of the line to represent x ≥ 1.
Lastly, let's graph the inequality 200x + 100y ≤ 700:
1) Rewrite the inequality as 2x + y ≤ 7.
2) Draw a line with a slope of -2 passing through the point (0, 7).
3) Shade the region below the line to represent 2x + y ≤ 7.
The solution set will be the overlap of the shaded regions from all three inequalities.
C) To find the number of nights you can spend at the resort and stay within your budget, we need to analyze the graph. Look for the region where the resort stays (x) are within your budget ($700). The graph will show the maximum number of nights you can spend at the resort while staying within your budget. Read the x-coordinate of the graph in that region to determine the maximum number of nights you can spend at the resort.