Zoe is creating “travel totes” and “bling baskets” as party favours for her sister Janine’s wedding. Janine has asked Zoe to make sure that there are at most 48 favours altogether and that there are at least 24 travel totes for her guests. If it costs $25 for every travel tote and $18 for every bling basket, what is the maximum amount Janine could expect to pay to create her wedding favours?
a. State the system of inequalities that represents this situation. Remember to define your variables
and include any non-negative constraints that are required.
b. What is the optimization equation?
c. Should your feasible region be stippled? Why or why not?
d. On graph paper, create the feasible region that represents this problem. Label your axes.
e. What is the maximum amount Janine could expect to pay for her wedding favours?
a. The system of inequalities that represents this situation can be defined as follows:
Let x represent the number of travel totes and y represent the number of bling baskets.
1. Total number of favours: x + y ≤ 48
2. Minimum number of travel totes: x ≥ 24
3. Non-negative constraints: x ≥ 0, y ≥ 0
b. The optimization equation in this case is the cost equation. We can calculate the cost as:
Cost = (cost per travel tote * number of travel totes) + (cost per bling basket * number of bling baskets)
= (25x) + (18y)
c. The feasible region should not be stippled because we are not looking for a specific point within the feasible region, rather we want to find the maximum amount Janine could expect to pay.
d. Unfortunately, as I am a text-based AI, I cannot create graphs. However, you can plot the feasible region on graph paper. The x-axis represents the number of travel totes (x) and the y-axis represents the number of bling baskets (y). Plot the inequalities x + y ≤ 48, x ≥ 24, x ≥ 0, and y ≥ 0 on the graph to create the feasible region.
e. To find the maximum amount Janine could expect to pay for her wedding favors, we need to find the corner points of the feasible region and evaluate the cost equation (25x + 18y) at each corner point. The corner point that gives the maximum cost would be the maximum amount Janine could expect to pay.
a. The system of inequalities that represents this situation is:
Let x be the number of travel totes and y be the number of bling baskets.
1) x + y ≤ 48 (at most 48 favours altogether)
2) x ≥ 24 (at least 24 travel totes)
b. The optimization equation is the cost equation:
Cost = 25x + 18y
c. No, the feasible region should not be stippled because it is not bounded.
d. Without specific values for the axes, it is not possible to create the graph.
e. The maximum amount Janine could expect to pay for her wedding favours depends on the specific values chosen for x and y within the feasible region. It cannot be determined without further information.