The table below describes the constraints on the total quantities of protein and carbohydrates, indicating that these quantities are fixed. There are two equations: one for the total quantity of protein and the other for the total quantity of carbohydrates.---| | **x, number of servings of Designer Whey** | **y, number of servings of Muscle Milk** | **Desired** ||---------------------------|-------------------------------------------|-----------------------------------------|---------------|| **Protein** | 18 grams per serving | 32 grams per serving | **580 grams** || **Carbohydrates** | 2 grams per serving | 16 grams per serving | **164 grams** || **Cost** | $0.50 per serving | $1.60 per serving | |---To find the first constraint equation, we focus on the "protein" row in the table.If $ x $ servings of Designer Whey (providing 18 grams of protein per serving) and $ y $ servings of Muscle Milk (providing 32 grams of protein per serving) are used, the total protein supplied can be expressed as:\[ (18)x + (32)y \text{ grams}. \]Given that the total desired protein is 580 grams, the equation describing the total protein supplied is:\[ 18x + 32y = 580. \]

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The table below shows that the two constraints are that the total quantities of protein and carbohydrates are fixed. One equation will describe the total quantity of protein in the mix and the other the total quantity of carbohydrates. x, number of servings of Designer Whey y, number of servings of Muscle Milk Desired 580 Protein 18 grams per serving 32 grams per serving grams 164 Carbohydrates 2 grams per serving 16 grams per serving grams Cost $0.50 per serving $1.60 per serving We use the "protein" row of the table to find the first constraint equation. If x servings of Designer Whey (supplying 18 grams of protein per serving) and y servings of Muscle Milk (supplying 32 grams of protein per serving) are used, then the total protein supplied is y grams. The total protein supplied is 580 grams, so an equation describing the total protein supplied is

The table below shows that the two constraints are that the total quantities of protein and carbohydrates are fixed. One equation will describe the total quantity of protein in the mix and the other the total quantity of carbohydrates. x, number of servings of Designer Whey y, number of servings of Muscle Milk Desired 580 Protein 18 grams per serving 32 grams per serving grams 164 Carbohydrates 2 grams per serving 16 grams per serving grams Cost $0.50 per serving $1.60 per serving We use the "protein" row of the table to find the first constraint equation. If x servings of Designer Whey (supplying 18 grams of protein per serving) and y servings of Muscle Milk (supplying 32 grams of protein per serving) are used, then the total protein supplied is y grams. The total protein supplied is 580 grams, so an equation describing the total protein supplied is

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The table below describes the constraints on the total quantities of protein and carbohydrates, indicating that these quantities are fixed. There are two equations: one for the total quantity of protein and the other for the total quantity of carbohydrates.

---

| | **x, number of servings of Designer Whey** | **y, number of servings of Muscle Milk** | **Desired** |
|---------------------------|-------------------------------------------|-----------------------------------------|---------------|
| **Protein** | 18 grams per serving | 32 grams per serving | **580 grams** |
| **Carbohydrates** | 2 grams per serving | 16 grams per serving | **164 grams** |
| **Cost** | $0.50 per serving | $1.60 per serving | |

---

To find the first constraint equation, we focus on the "protein" row in the table.

If $ x $ servings of Designer Whey (providing 18 grams of protein per serving) and $ y $ servings of Muscle Milk (providing 32 grams of protein per serving) are used, the total protein supplied can be expressed as:

\[ (18)x + (32)y \text{ grams}. \]

Given that the total desired protein is 580 grams, the equation describing the total protein supplied is:

\[ 18x + 32y = 580. \]

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