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KozzyKoz
08.10.2020 •
Mathematics
I have just learned linear programming and need extra help finding the constraints (there are four). The Wheelie Manufacturing Company makes bicycles and tricycles. In order to meet demands of its retailers, the company must make at least 20 bicycles and 30 tricycles each day. At most twice as many tricycles as bicycles can be made in a day. A total of only 90 bicycles and tricycles can be made each day. The profit on each bicycle is $17 and the profit on each tricycle is $21. How many bicycles and tricycles should be made in order to maximize the profits?
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Ответ:
To maximize profit the company will have to produce 30 bicycles and 60 tricycles
Step-by-step explanation:
yes this is a linear programming program
let us represent bicycles as x
and tricycles as y
the objective function is
maximize
17x+21y=P
constraint
20m+30n=90
"At most twice as many tricycles as bicycles can be made in a day"
so n=2
let us find x when the company produces maximum y
so we have to substitute y=2 in the constraint
20m+30(2)=90
20m+60=90
divide through by 10 we have
2m+6=9
2m=9-6
2m=3
divide through by 2 we have
m=1.5
we can now see that at maximum
the company produces
tricycles=20m
tricycles=20(1.5)
tricycles= 30
and
bicycles= 30m
bicycles= 30(2)
bicycles= 60
now let us substitute x=30 and y =60 in the objective function we have
17(30)+21(60)=P
510+1260=P
P=$1770
Ответ:
Six
Step-by-step explanation:
Find the greatest common factor of each number.
Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30
Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24
The greatest common factor of 30 and 24 is 6.
Jane can make six fruit baskets if she divides the fruit evenly among them.