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?
- $2:1:3$
- $4:1:2$
- $2:1:4$
- $3:1:2$
- $4:1:1$