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3 years ago

R=a(x+b)/3 solve for x

Mathematics

2 answers:

Len [333]3 years ago

8 0

R=(ax+ab)/3 is the answer.

cluponka [151]3 years ago

8 0

R=a(x+b)/3
r=ax +ab
---------
3
3r=ax+ab divide by a
3r/a = x+b
3r/a-b=x

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(From Textbook) A company makes dog food out of chicken and grain. Chicken has 10 grams of protein and 5 grams of fat per ounce,

Doss [256]

Answer:

The company use 0 ounces of chicken and 100 ounces of grain in each bag of dog food in order to minimize cost.

Step-by-step explanation:

Let x be the number of ounces of chicken

let y be the number of ounces of grains

We are given that Chicken has 10 grams of protein and 5 grams of fat per ounce.

Chicken has protein in 1 ounce = 10

Chicken has protein in x ounces = 10x

Chicken has fat in 1 ounce = 5

Chicken has fat in x ounces = 5x

We are also given that grain has 2 grams of protein and 2 grams of fat per ounce

Grain has protein in 1 ounce = 2

Grain has protein in y ounces = 2y

Grain has fat in 1 ounce = 2

Grain has fat in y ounces =2y

Now we are given that . A bag of dog food must contain at least 200 grams of protein and at least 150 grams of fat.

So, equation becomes:

$10x+2y\geq 200$ ---A

$5x+2y\geq 150$ ---B

Since x and y represent the ounces .

So, $x\geq 0$ ---C and $y\geq 0$ ----D

Plot A ,B ,C and D on the graph

Refer the attached graph so , the corner points are (0,100),(10,50) and (30,0)

We are also given that chicken costs 10 cents per ounce and grain costs 1 cent per ounce

So, Cost function becomes : $c=10x+y$

At(0,100)

$c=10x+y$

$c=10(0)+100$

$c=100$

At(10,50)

$c=10x+y$

$c=10(10)+50$

$c=150$

At(30,0)

$c=10x+y$

$c=10(30)+0$

$c=300$

Minimum cost is 100 cents at (0,100)

So, the company use 0 ounces of chicken and 100 ounces of grain in each bag of dog food in order to minimize cost.

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