Please help this question is from my unit on linear programing and I'm having trouble completing it.

Question

A company manufactures bicycles and tricycles. The total number of frames the company manufactures cannot exceed 80 per month. It takes the company 1 hour to assemble a bicycle and 2 hours to assemble a tricycle. The assembly machine is only available for 100 hours each month. If the company makes a profit of $50 on each bicycle and $70 on each tricycle, determine the number of bicycles and tricycles that will maximize profits each month. Indicate the maximum profit the company can make each month.
This is what I have so far: x=#of bicycles y=#of tricycles
x>=0 y>=0 P=50x +70y
Now I don't know what to do. Any help would be greatly appreciated. Thanks

Answer 1

You need

b+t </= 80 (frames limit)

b + 2 t </= 100 (machine hour limit)

graph those t on x axis, b on y axis

they cross at
(80-t)+2 t = 100
t = 20
b = 60
look at resulting quadrilateral including axes, must be inside it

so we have three realistic (t,b) points
(0,80)
(20,60)
(50,0)
check
p = 70 t + 50 b
at those three points
which gives max p?