As a restaurant owner there are many decisions that you need to make on a daily basis, such as where to keep inventory levels. You wish to replenish your stock of dishes by purchasing 250 sets for your restaurant. You have two dish design from which to choose. One design costs $20 per set and the other $45 per set. If you only have $6,800 to spend, how many of each design should you order?

Question

As a restaurant owner there are many decisions that you need to make on a daily basis, such as where to keep inventory levels. You wish to replenish your stock of dishes by purchasing 250 sets for your restaurant. You have two dish design from which to choose. One design costs $20 per set and the other $45 per set. If you only have $6,800 to spend, how many of each design should you order?

Let x = the number of sets of $20 dishes and y = the number of sets of $45 dishes.

•Solve the equations for the different dish designs to be ordered with the desired technique: graphing, substitution, elimination, matrix.
•Explain how to check your solution for both equations.
How can I graph this word problem

Answer 1

http://www.jiskha.com/display.cgi?id=1289061343

Answer 2

To graph this word problem, we need to plot the possible combinations of the number of sets of $20 dishes (x) and the number of sets of $45 dishes (y) that can be ordered within the given budget.

First, let's set up the equations based on the information provided:

1. The cost of x sets of $20 dishes is given by: 20x
2. The cost of y sets of $45 dishes is given by: 45y

We need to consider two constraints:
1. The total number of sets of dishes should be 250: x + y = 250
2. The total cost should not exceed $6,800: 20x + 45y ≤ 6,800

Now, we can graph these equations on a coordinate plane:

Step 1: Plot the constraint x + y = 250
- Select a range for x and y that make sense in the context of the problem, for example, 0 to 250.
- Choose convenient x and y values and plot them on the graph.
- Connect the dots to create a straight line passing through those points.

Step 2: Plot the constraint 20x + 45y ≤ 6,800
- Rearrange the equation to y ≤ (6,800 - 20x)/45.
- Select several x-values and calculate the corresponding y-values based on the equation.
- Plot these points and connect them to form a boundary line.

Step 3: Shade the area that satisfies both constraints.
- Identify the common area between the two lines on the graph and shade it.

Step 4: Find the coordinates of the feasible points.
- The feasible points are the coordinates within the shaded area.
- Each point represents a combination of x and y that satisfies the given constraints.

To find the optimal solution, locate the point(s) within the feasible region that maximize the number of sets of dishes while staying within the budget.