I'm doing linear programming and I'm having trouble with this one problem.
The Backstage Dance Studio director must plan for and operate many different classes, 7 days a week, at all hours of the day. Saturday is very important day for younger students, and each Saturday class fills up quickly.
a. To plan the Saturday schedule, the director has to consider these facts.
A. It's not easy to find enough good teachers, so the studio can offer at most 8 tap classes and at most 5 jazz classes.
B. The studio has limited classroom space, so it can offer a total of at most 10 classes for the day.
C. The studio makes profit of $150 from each tap class and $250 from each jazz class.
What are the variables in this situation
Write algebraic inequalities giving the constraints on the variables.
T = number of tap classes
J = number of Jazz classes
Now the constraints:
"at most 8 tap classes and at most 5 jazz classes. "
T≥0
T≤?
J≥0
J≤?
"at most 10 classes for the day. "
T+J≤?
" profit of $150 from each tap class and $250 from each jazz class. "
Objective function = Revenue = 150T + 250J
Now can you proceed?
Post any time if you have questoins.
Also, even though it is obvious,
T≥0 and J≥0 are required conditions.
The variables in this situation are the number of tap classes and the number of jazz classes offered on a Saturday.
Let's write the algebraic inequalities to represent the constraints based on the given facts:
1. The studio can offer at most 8 tap classes:
Number of tap classes ≤ 8
2. The studio can offer at most 5 jazz classes:
Number of jazz classes ≤ 5
3. The studio can offer a total of at most 10 classes for the day:
Number of tap classes + Number of jazz classes ≤ 10
Note that the inequalities represent the upper limits or maximum number of classes that can be offered based on the constraints provided.
t < or equal to 8
J < or equal to 5
t+J < or equal to 10
Now I understand.