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14.02.2020 •
Business
Maggie Stewart loves desserts. But, due to weight and cholesterol concerns, she has decided that she must plan her desserts carefully. There are two possible desserts she is considering: snack bars and icecream. After reading the nutrition labels on the snack bar and ice-cream packages, she learns that each serving of a snack bar weighs 37 grams and contains 120 calories and 5 grams of fat. Each serving of icecream weighs 65 grams and contains 160 calories and 10 grams of fat. Maggie will allow herself no more than 450 calories and 25 grams of fat in her daily desserts, but because she loves desserts so much, she requires at least 120 grams of dessert per day.
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Ответ:
The option that maximizes Maggie's taste index is 1 snack bar and 2 ice creams
Explanation:
snack bar ice cream
37 grams 65 grams
120 calories 160 calories
5 grams of fat 10 grams of fat
Maggie wants to consume up to 450 calories and 25 grams of fat, but she needs at least 120 grams of dessert per day. Ice cream taste 95, snack bars 85.
maximize taste index = [85(37X) + 95(65Y)] / (37X + 65Y)5X + 10Y ≤ 25 ⇒ CONSTRAINT 1120X + 160Y ≤ 450 ⇒ CONSTRAINT 237X + 65Y ≥ 120 ⇒ CONSTRAINT 3X ≥ 0 ⇒ CONSTRAINT 4Y ≥ 0 ⇒ CONSTRAINT 5maximum possible combinations following constraint 1, 4 AND 5:
option 1: 1 snack bar - 2 ice creams (5 + 20 = 25)option 2: 2 snack bars - 1 ice cream (10 + 10 = 20)option 3: 3 snack bars - 1 ice cream (15 + 10 = 25)possible combinations following constraint 2:
option 1: 1 snack bar - 2 ice creams (120 + 320 = 440)option 2: 2 snack bars - 1 ice cream (240 + 160 = 400)possible combination following constraint 3:
option 1: 1 snack bar - 2 ice creams (37 + 130 = 167)option 2: 2 snack bars - 1 ice cream (74 + 65 = 139)since we only have two possibilities, we can calculate which one generates the highest taste index
maximize taste index = [85(37X) + 95(65Y)] / (37X + 65Y)
option 1: 1 snack bar - 2 ice creams = [85(37) + 95(130)] / (37 + 130) = (3,145 + 12,350) / 167 = 92.78option 2: 2 snack bars - 1 ice cream = [85(74) + 95(65)] / (74 + 65) = (6,290 + 6,175) / 139 = 89.68Ответ: