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.
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?
1 answer