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Algebra

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A florist designs two high profit arrangement a funeral wreath and a bridal centerpiece. The company'[s employees can complete up to 17 arrangements each day using up to 26 total person hours of labor. It takes 4 person hours to complete 1 funeral wreath and 1 person hour to complete 1 bridal centerpiece. How many of each type of arrangements should the florist produce daily for maximum profit, if the profit on a funeral wreath is $65 and the profit on a bridal centerpiece is $42?
To maximise profit we need to do
Max( 65x + 42y)
Where x = Funeral Wreath ( FW)
y = Bridal Centerpiece ( CP )
x + y <= 17 such that we maximise the profit.
Now we have a few options to add on to the total man hours that is 26.
FW = 4 person hour , CP = 1 person hour
So, FW will be in multiple of 4 and CP in multiple of 1.
We check how many combinations are possible.
Option 1:Person Hour.... FW = 24 CP= 2.............Total numbers made x = 6 y = 2
Option 2:Person Hour.... FW = 20 CP = 4.............Total numbers made x = 5 y= 4
Option 3:Person Hour.... FW = 16 CP = 10.............Total numbers made x = 4 y = 10
Option 4:Person Hour.... FW = 12 CP = 14.............Total numbers made x = 3 y = 14
Option 5:Person Hour.... FW = 8 CP = 18.............Total numbers made x = 2 y = 18
Option 6:Person Hour.... FW = 4 CP = 22.............Total numbers made x = 1 y = 22
Option 7:Person Hour.... FW = 0 CP = 26...............Total numbers made x = 0 y = 26
But we know, sum of x and y should not exceed 17, hence Option 5 to Option 8th are ruled out.
Clearly, now we see which option maximises profit. By putting values of x and y for Max( 65x + 42y)
Option 1: Max( 65x + 42y) = Max ( 65 * 6 + 42 * 2 ) = 474
Similarly calculating for all options we will get that for x = 3 and y = 14 the value of profit maximises.
Florist makes large bouquets and small bouquets. the workers can make at most 500 bouquets per day. Each large bouquet requires 80 flowers and small bouquets requires 40 flowers. there are 1500 plants available. The income from each large bouquets is $250 and from each small bouquet is $125. How many of each size bouquet should be made to maximize income?
SOLUTION:
Objective function:
Constraints:
Graph:
Vertices:
Optimization:
Pleas make it a paid questions its not small !!! $5 would be fine !
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