A computer store is placing an order for computers and tablets. Each computer costs $875, and each tablet costs $235. The store can spend at most $10,000 for these computers and tablets. The computer store has a limited amount of space for displaying the new computers and tablets. Each computer takes up 4 square feet of space, and each tablet takes up 3 square feet of space. The store has only 45 square feet of display space available for the new computers and tablets. The system of inequalities shown can be used to determine possible combinations of computers, x, and tablets, y, the store can order.
875x + 235y ≤ 10,000
4x +3y ≤ 45
Which combinations of computers, x, and tablets, y, can the computer store order?
To determine the combinations of computers and tablets the computer store can order, we need to find the solutions to the system of inequalities:
875x + 235y ≤ 10,000
4x +3y ≤ 45
We can solve this system by graphing.
First, let's graph the equation 875x + 235y ≤ 10,000.
Solving for y, we have:
y ≤ (10,000 - 875x) / 235
This gives us the slope-intercept form of the equation for y, where the slope is -(875/235) ≈ -3.72 and the y-intercept is 10,000/235 ≈ 42.55.
So, we can plot this line on the graph with the slope -3.72, and y-intercept 42.55.
Now, let's graph the equation 4x + 3y ≤ 45.
Solving for y, we have:
y ≤ (45 - 4x) / 3
This gives us the slope-intercept form of the equation for y, where the slope is -(4/3) ≈ -1.33 and the y-intercept is 45/3 = 15.
So, we can plot this line on the graph with the slope -1.33 and y-intercept 15.
Now, we can shade the region on the graph that satisfies both inequalities.
The region where y is less than or equal to (10,000 - 875x) / 235 is below the line for 875x + 235y ≤ 10,000.
The region where y is less than or equal to (45 - 4x) / 3 is below the line for 4x + 3y ≤ 45.
The overlapping shaded region represents the combinations of computers (x) and tablets (y) that the store can order.