Question

The Frivoli can produce either 30 pounds of spaghetti and no meatballs or 50 pounds of meatballs and no spaghetti or any combination in between. The Frivoli can produce 40 pounds of spaghetti and no meatballs or 30 pounds of meatballs and no spaghetti. Assuming all production possibilities frontiers are straight lines. Draw a frontier for each. Do I simply put a a vertical line for Frivoli connecting 30 for spaghetti and 50 for meatballs, making a vertical line. and do the same for the other?
HELP

Answer 1

I put S for spaghetti on my vertical (Y) axis) and M for Meatball on my horizontal (x) axis then I connected 30 on the vertical axis with 50 on the horizontal axis to get a slanting straight line from (0,30) to (50,0). My feasible area is between the origin and the line in the first quadrant (no negative spaghetti or meatballs)
Same with the other one from (0,40) to (30,0)

Answer 2

Now I get those lines hit at about (13.6 , 21.8)
so inside the region defined by
(0,0), (0,30), (13.6, 21.8) (0,30)
either machine could do the work (intersection of sets)

inside the region defined by
(0,0), (0,40), (13.66, 21,8), (50,0)
one machine, or the other, or both could do the work
(union of sets)