Question

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?​

Answer 1

To maximize profit the company will have to produce 30 bicycles and 60 tricycles

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