Ten girl students of a post-graduate science college are residing in the same hostel as the other 200 boy students because the college does not provide separate accommodation for girl students. The boys are rather troublesome and the girls, therefore, want to keep them at a safe distance. With this in view, the girls have discovered two chemicals available in the laboratory, nicknamed ‘Ugh’ and ‘No-no’, which can be mixed in certain proportion with bathing shampoo and facial cream. Amazingly, these chemicals have repelling properties only for the male sex with no effects at all for the female sex.

Now, for proper effect, the shampoo needs 1.1% of Ugh and 0.1% of No-no to be mixed with it. The Facial Cream needs 0.5% and 0.25% of Ugh and No-no, respectively, for the desired effect.

Every girl needs a minimum of 2 ml of shampoo and 1 ml of facial cream every day. The price of Shampoo and Cream in the market are respectively Rs. 10 per 100 ml and Rs. 18 per 20 ml. The amounts of Ugh and No-no that can be obtained from the laboratory are limited to 15 ml and 5 ml (per month) only, due to very limited yields of these special chemicals. If the expenses on these cosmetics are to be no more than Rs. 450 per month, and if the proportionate ‘repel’ effects of Shampoo and facial cream are 2:3, then what are the optimal quantities of shampoo and facial cream the girls should procure?

(Assume: (i) A month has 30 days.

(ii) Ugh and No-no are available free.

(iii) The college has no male teachers, surprisingly.)