If a bedroom set sells for $10,000 and a living room set sells for $18,000,determine the number of bedroom sets and living room sets that must be sold to maximize the amount collected.
I'm not sure what I need to do to set this up.
To determine the number of bedroom and living room sets that must be sold to maximize the amount collected, we need to set up an optimization problem.
Let's denote:
- x as the number of bedroom sets sold
- y as the number of living room sets sold
We are given that a bedroom set sells for $10,000 and a living room set sells for $18,000.
The total collected amount can be calculated by multiplying the number of sets sold by the price of each set and summing them up. Therefore, the total amount collected (C) can be expressed as:
C = 10,000x + 18,000y
Now, we want to maximize the amount collected. However, there might be some constraints on the number of sets that can be sold. We need to know if there are any constraints given in the problem statement, such as limited supply or demand requirements. Without these constraints, we cannot determine the optimal solution. Could you provide any additional information?