A person wants to purchase two types of items, A and B, from a shop. She has $200 to spend, and she has to purchase at least 10 items. If the price of one unit of each A and B is $10 and $30, respectively, represent this
problem graphically.
To represent this problem graphically, we can use a coordinate plane. Let's plot the number of item A on the X-axis and the number of item B on the Y-axis.
First, we need to determine the feasible region, which represents all the possible combinations of items A and B that can be purchased within the given constraints.
The person has $200 to spend. The price of one unit of A is $10, so the maximum number of item A she can purchase is 200 / 10 = 20. Similarly, the price of one unit of B is $30, so the maximum number of item B she can purchase is 200 / 30 = 6.67 (approximated to 6 since the person cannot buy fractional items).
Now let's plot the points (x, y) where x represents the number of item A and y represents the number of item B. The feasible region will be within the following boundaries:
- x can range from 0 to 20 (inclusive), representing the potential quantities of item A.
- y can range from 0 to 6 (inclusive), representing the potential quantities of item B.
The feasible region will be a rectangle bounded by the coordinates (0, 0), (20, 0), (20, 6), and (0, 6).
Now, to represent the constraint of purchasing at least 10 items, we need to draw a line, let's call it line L1, that passes through the points (10, 0) and (0, 10). This line represents all the possible combinations where the sum of item A and B is equal to or greater than 10.
Finally, shade the area below the line L1 and within the feasible region rectangle. This shaded area represents the valid combinations of items A and B that satisfy both the budget constraint and the requirement of purchasing at least 10 items.
Note: The graph can be drawn on a piece of paper or using graphing software to get a visual representation of the problem.