Abiologist wishes to feed laboratory rabbits a mixture of two types of foods. type 1 contains 8g of fat, 12g of carbs, and 2g of protein per ounce. type 2 contains 12g of fat, 12g of carbs, and 1g of protein per ounce. type 1 costs $0.20 per ounce and type 2 costs $0.30 per ounce. the rabbits each receive a daily minimum of 24g of fat, 36g of carbs, and 4g of protein, but get no more than 5 oz. of food per day. if each food type must be fed, how many ounces of each food type should be given to satisfy the dietary requirements at a minimum cost? (hint: there are 4 constraints.)

we have minimize cost by feeding the rabbits 3 ounces  of feed 1 and 0 ounces of feed 2.

Explanation:

let x be the ounces of feed 1

let y be the ounces of feed 2

according to the information we have following inequalities  

Fat grams:

Carb grams:

Protein grams:

Total food:

for cost we have

C = 0.20x + 0.30y

Thus, we have the limitation of:

plotting all inequalities we have found pentagon with following points

(0,5)

C = 0.20(0) + 0.30(5) = 1.50

(0,4)

C = 0.20(0) + 0.30(4) = 1.20

(1,2)

C = 0.20(1) + 0.30(2) = 0.80

(3,0)

C = 0.20(3) + 0.30(0) = 0.60

(5,0)

C = 0.20(5) + 0.30(0) = 1.00

Thus, we have minimize cost by feeding the rabbits 3 ounces  of feed 1 and 0 ounces of feed 2.

answer: b. reduces acid production to slow digestion

one pad at the centre of the baby's chest and the other pad on the centre of the baby's upper back.

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