A certain diet consists of milk, beans and oranges. In order for the diet to wor

Question

A certain diet consists of milk, beans and oranges. In order for the diet to work, there must be minimum levels of niacin, thiamin, and vitamin C that the individual receives every day. The table below shows how much of each vitamin/mineral is in milk, beans and oranges and it shows the minimum daily amounts needed. The goal is to minimize the cost and the cost for milk is $2, the cost for beans is $0.20, and the cost for oranges is $0.25. To two decimal places, find the amount of oranges that should be in this diet.

Explanation / Answer

Let say total cost = Milk amount * cost of mile + Beans amount * cost for beans + Vitamin C amount * Cost for oranges

Lets say milk amount is x , Beans amount is y and Vitaminc amount is z units

so total cost = 2x + 0.2y + 0.25 z

so we have to minimize the total cost

Here constraints are

3.2 x + 4.9 y + 0.8z > 13....(i)

1.12 x + 1.3 y + 0.19 z > 1.5....(ii)

32x + 93 z > 45 ....(iii)

Total Cost = $0.63578;

Amount of MIlk = 0,

Amount of Beans = 2.57406,

Amount of Oranges = 0.483871

Amount of oranges should be in the diet = 0.48

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