A dairy company gets milk from two dairies and then blends the milk to get the desired amount of butterfat. Milk from dairy I costs $2.40 per gallon, and milk from dairy II costs $0.80 per gallon. At most $144 is available for purchasing milk. Dairy I can supply at most 50 gallons averaging 3.9% butterfat, and dairy II can supply at most 90 gallons averaging 2.9% butterfat. Answer parts a and b. a. How much milk from each supplier should the company buy to get at most 100 gallons of milk with the maximum amount of butterfat? The company should buy 40 gallons from dairy I and 60 gallons from dairy II. What is the maximum amount of butterfat? 330 gallons (Type an integer or a decimal.) b. The solution from part a leaves both dairy I and dairy II with excess capacity. Calculate the amount of additional milk each dairy could produce. The excess capacity of dairy I is 10 gallons, and for dairy II it is 30 gallons. Is there any way all this capacity

a) i The company should buy 40 gallons from dairy I and 60 gallons from dairy

ii) What is the maximum amount of butterfat? The total amount of butterfat from Diary I and Diary II = 3.12% + 1.93%

=5.05%

b.The excess capacity of dairy I is 10 gallons, and for dairy II it is 30 gallons.

Step-by-step explanation:

a. How much milk from each supplier should the company buy to get at most 100 gallons of milk with the maximum amount of butterfat?

From the question, we are told that:

Milk from dairy I costs $2.40 per gallon, Milk from dairy II costs $0.80 per gallon.

Let's represent:

Number of gallons of Milk from dairy I = x

Number of gallons of Milk from dairy II = y

At most $144 is available for purchasing milk.

$2.40 × x + $0.80 × y = 144

2.40x + 0.80y = 144 Equation 1

x + y = 100 Equation 2

x = 100 - y

2.40(100 - y) + 0.80y = 144

240 - 2.4y + 0.80y = 144

-1.60y = 144 - 240

-1.6y = -96

y = -96/-1.6

y = 60

From Equation 2

x + y = 100 Equation 2

x + 60 = 100

x = 100 - 60

x = 40

Therefore, since number of gallons of Milk from dairy I = x and number of gallons of Milk from dairy II = y

The company should buy 40 gallons from dairy I and 60 gallons from dairy

II. What is the maximum amount of butterfat?

From the question

Dairy I can supply at most 50 gallons averaging 3.9% butterfat,

50 gallons = 3.9% butterfat

40 gallons =

Cross Multiply

= 40 × 3.9/50

= 3.12%

Dairy II can supply at most 90 gallons averaging 2.9% butterfat.

90 gallons of milk = 2.9% butter fat

60 gallons of milk =

Cross Multiply

= 60 × 2.9%/90

=1.9333333333%

≈ 1.93%

The total amount of butterfat from Diary I and Diary II = 3.12% + 1.93%

=5.05%

b. The solution from part a leaves both dairy I and dairy II with excess capacity. Calculate the amount of additional milk each dairy could produce.

Excess capacity of Diary I =

50 gallons - 40 gallons = 10 gallons

Excess capacity of Diary II =

90 gallons - 60 gallons = 30 gallons

Therefore, the excess capacity of dairy I is 10 gallons, and for dairy II it is 30 gallons.

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