I need help with my math review. How do I correctly solve this problem using Linear Programming?

Question

Here is the question:
A toy manufacturer is introducing two new dolls, My First Baby and My Real Baby. IN one hour, the company can produce 8 First Babies or 20 Real Babies. Because of demand, the company produces at least twice as many First Babies as Real Babies. The company spends no more than 48 hours per week making these two dolls. The profit on each First Baby is $3.00, and the profit on each Real Baby is $7.50. Find the number and type of dolls that should be produced to maximize profit.

I used F for fthe number of First Babies and R for the number of Real Babies. All I am sure of is that F is greater than or equal to zero, R is greater than or equal to zero and that F is greater than or equal to 2R. I am unsure of the other equations needed to be graphed, since I keep getting the wrong answers. The correct answer is 320 First Babies and 160 Real Babies. How do you get that as a maximum value?

Answer 1

This is what i make of it :

F >= 0
R >= 0
F >= 2R
F/8 + R/20 <= 48
max P(F,R) = 3F + 7.5R

"draw the lines , the theory says that your max is on an corner." or use a tableau method.

Answer 2

P = 3F + 7.5R = profit
F <= 384
F >= 2R --> R =< 192
F/8 + R/20=< 48 --> 5F +2R <= 1920 --> F <= -2R/5+384
Shade the area above line F= 2R, below line F=2R/5 +384, to left of line R= 192, below line F=384, above R=0 and to right of F =0. Evaluate profit at each intersection point and you have it.

Answer 3

Huh? My brain hurts just reading that problem.