Fruit Juice linear programming question

Question

A bottler uses three juices - pineapple, orange, and grapefruit- to make two juice mixtures, pineapple-orange and pineapple-grapefruit, sold in 1-quart bottles. The profit is 50 cents per bottle of pineapple-orange and 40 cents per bottle of pineapple-grapefruit. Each mixture is made by using equal proportions of the two juices in its name. The amounts of juice on hand are 100 quarts of pineapple juice, 70 quarts of grapefruit, and 40 quarts of orange juice. How many of each juice mixture should be produced to maximize profits?

Answer 1

50 per PAO, 40 per PAG, 0 per GO

100 quarts of PA

70 of G

40 of O

total quarts = 210

most profit is made on PAO, but since PA=0, the mixture will be 70 of G and 70 of PA, leaving another 30 quarts to mix with O, meaning 30 of PA with 30 of 0. profit is 50(140) + 40(60) = 7000 + 2400 = $9400

Total maximum profit = $9400

That leaves 10 quarts of Orange Juice unused. But if you used any of it to mix with pineapple juice that reduces profit by $20 per quart.

31 quarts O with 31 PA has profit of 62(40) = 2480 + profit on 69G with 69PA = 50(138) = 6900

2480 + 6900 = $9380

PA:G = 70:70

PA;O = 30:30

to obtain maximum profit of $9,400