(This is the info for the question NOT the actual question)
A furniture company displays bedroom sets which require 21 square meters of space and living room sets which require 42 square meters of space. The company, which has 546 square meters of avalible space, wants to display at least 6 bedroom sets and at least 5 living room sets.
Question:
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.
16 beds * 21 square meters of space = 336
5 living * 42 square meters of space = 210
add those two up and get the total availible space of 546
16 * 10,000 = $160,000
5 * $18,000 = $90,000
= $250,000 maxed out
So they would need to sell 16 bedroom sets and 5 living room sets
You seem to have answered the question. The method is to realize that bedroom sets sell for more per floor area; therefore, once the required minimum number of living room sets(5)is displayed, to use all remaining space for bedroom sets. There is room for 16.
draw the graph showing the feasible region. Label the coordinates of the vertices of the feasible region.
To solve this problem and determine the number of bedroom sets and living room sets that must be sold to maximize the amount collected, we need to consider the available space and the selling price for each set.
First, let's calculate the total space required for displaying the bedroom and living room sets. We are given that each bedroom set requires 21 square meters of space, and each living room set requires 42 square meters. So, if we multiply the number of bedroom sets by 21 and the number of living room sets by 42, we can calculate the total space required.
Number of bedroom sets * 21 = total space required for bedroom sets
Number of living room sets * 42 = total space required for living room sets
Next, we need to ensure that the total space required for both sets does not exceed the available space. We are given that the company has 546 square meters of available space. So, the total space required for both sets should be less than or equal to 546.
Now, let's look at the selling prices for the bedroom and living room sets. We are told that a bedroom set sells for $10,000, and a living room set sells for $18,000. To maximize the amount collected, we want to sell the maximum number of sets.
To find the maximum number of sets that can be sold, we divide the available space by the space required for each set. This will give us the maximum number of sets that can be displayed based on the available space.
Maximum number of bedroom sets = available space / space required for a bedroom set
Maximum number of living room sets = available space / space required for a living room set
Finally, we multiply the maximum number of bedroom sets by the selling price for a bedroom set and the maximum number of living room sets by the selling price for a living room set. This will give us the maximum amount of money that can be collected.
Maximum amount collected = (maximum number of bedroom sets * selling price for a bedroom set) + (maximum number of living room sets * selling price for a living room set)
By performing these calculations, we can determine the number of bedroom sets and living room sets that must be sold to maximize the amount collected.