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Answer the following question based on the information given below:

A health-drink company’s $\text{R & D}$ department is trying to make various diet formulations, which can be used for certain specific purposes. It is considering a choice of $5$ alternative ingredients $\text{(O, P, Q, R and S)},$ which can be used in different proportions in the formulations. The table below gives the compositions of these ingredients. The cost per unit of each of these ingredients is $\text{O: 150, P: 50, Q: 200, R: 500, S: 100.}$

  Composition
Ingredient Carbohydrate% Protein % Fat % Minerals%
O 50 30 10 10
P 80 20 0 0
Q 10 30 50 10
R 5 50 40 5
S 45 50 0 5

In what proportion $\text{P, Q}$ and $\text{S}$ should be mixed to make a diet having at least $60\%$ carbohydrate at the lowest cost per unit?

  1. $2:1:3$
  2. $4:1:2$
  3. $2:1:4$
  4. $3:1:2$
  5. $4:1:1$
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Answer $: \text{(E)}$

 We need at least $60\%$ carbohydrate at the lowest cost per unit

percentage of carbohydrate here $(80 * 4 + 10 + 45 ) / 6 = 62.5 > 60\%$
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