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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 $\text{O: 150, P: 50, Q: 200, R: 500, S: 100.}$

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

Which among the following is the formulation having the lowest cost per unit for a diet having $10\%$ fat and at least $30\%$ protein? This diet has to be formed by mixing two ingredients.

  1. $\text{P and Q}$
  2. $\text{P and S}$
  3. $\text{P and R}$
  4. $\text{Q and S}$
  5. $\text{R and S}$
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