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.
The more you sell, of either type of furniture set, the more money you collect. You must be omitting some information.
no that's all my book says
To set up this problem, we need to define some variables and constraints. Let's say 'x' represents the number of bedroom sets and 'y' represents the number of living room sets.
Now, let's determine the objective function and the constraints.
Objective function:
We want to maximize the amount collected, which is given by the formula:
Amount collected = (Price of bedroom set * Number of bedroom sets) + (Price of living room set * Number of living room sets)
Mathematically, this can be written as:
Amount collected = (10,000 * x) + (18,000 * y)
Constraints:
1. The number of bedroom sets and living room sets should be non-negative: x ≥ 0, y ≥ 0.
2. There may be other constraints based on the available stock or market demand, but these are not specified in the question.
To summarize:
Objective function: Amount collected = (10,000 * x) + (18,000 * y)
Constraints: x ≥ 0, y ≥ 0
Now, we can solve this problem using optimization techniques to find the values of x and y that maximize the amount collected.