Question

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.

Answer 1

Maggie can have a maximum of 3 snack bars and 1 ice cream serving while staying within her daily calorie and fat limits.

Step-by-step explanation:

Maggie should calculate the number of snack bars and ice creams she can have while staying within her daily calorie and fat limits. Let's start with the snack bars:

Each serving of a snack bar weighs 37 grams and contains 120 calories and 5 grams of fat. Since she needs at least 120 grams of dessert per day, she can have a maximum of 120/37 = 3.24 servings of snack bars. However, we need to consider the calorie and fat limits as well.

For calories, Maggie should try to consume no more than 450 calories per day. Each snack bar contains 120 calories, so she can have a maximum of 450/120 = 3.75 snack bars. However, since she needs at least 120 grams of dessert, she can only have 3 snack bars.

For fat, Maggie should try to consume no more than 25 grams per day. Each snack bar contains 5 grams of fat, so she can have a maximum of 25/5 = 5 snack bars. However, since she needs at least 120 grams of dessert, she can only have 3 snack bars.

Now, let's calculate the number of ice creams:

Each serving of ice cream weighs 65 grams and contains 160 calories and 10 grams of fat. Since she needs at least 120 grams of dessert per day, she can have a maximum of 120/65 = 1.85 servings of ice cream. However, we need to consider the calorie and fat limits as well.

For calories, Maggie should try to consume no more than 450 calories per day. Each ice cream serving contains 160 calories, so she can have a maximum of 450/160 = 2.81 servings of ice cream. However, since she needs at least 120 grams of dessert, she can only have 1 serving of ice cream.

For fat, Maggie should try to consume no more than 25 grams per day. Each ice cream serving contains 10 grams of fat, so she can have a maximum of 25/10 = 2.5 servings of ice cream. However, since she needs at least 120 grams of dessert, she can only have 1 serving of ice cream.

In summary, Maggie can have a maximum of 3 snack bars and 1 ice cream serving while staying within her daily calorie and fat limits.

Answer 2

The option that maximizes Maggie's taste index is 1 snack bar and 2 ice creams

Step-by-step 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 1
• 120X + 160Y ≤ 450 ⇒ CONSTRAINT 2
• 37X + 65Y ≥ 120 ⇒ CONSTRAINT 3
• X ≥ 0 ⇒ CONSTRAINT 4
• Y ≥ 0 ⇒ CONSTRAINT 5

maximum 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 = 92.78
• option 2: 2 snack bars - 1 ice cream = [85(74) + 95(65)] / (74 + 65) = (6,290 + 6,175) / 139 = 89.68