Question

An individual needs a daily supplement of at least 420 units of vitamin C and 170 units of vitamin E and agrees to obtain this supplement by eating two foods, I and II. Each ounce of food I contains 32 units of vitamin C and 10 units of vitamin E, while each ounce of food II contains 20 units of vitamin C and also 14 units of vitamin E. The total supplement of these two foods must be at most 28 ounces. Unfortunately, food I contains 27 units of cholesterol per ounce and food II contains 13 units of cholesterol per ounce. Find the appropriate amounts of the two food supplements so that cholesterol is minimized.

Answer 1

Answer:

To obtain equivalent amount from both foods we can eat 10 ounces of Food I and 5 Ounces of food II

To obtain minimum cholesterol, the individual should eat only 21 ounces of food II and zero ounce of food for the daily supplement of the individual

Step-by-step explanation:

Food I contains 32×C + 10×E per ounce

Food II contains 20×C + 14×E  

Here we have X × (Food I) + Y × (Food II) = 420 C + 170 E

32·X + 20·Y = 420 C

10·X + 14·Y = 170 E

Therefore

X = 10 and Y = 5

To minimize the cholesterol, we can increase amount of Food II to get

21 ounces of food II gives

420 units of vitamin E and 294 units of vitamin E with 273 units of cholesterol.