3.

(a) Shady Spring mineral water is sold as containing no more than 20 ppb (parts per billion by mass) of lead. It is a blend of three waters: A, B, and C. Water A contains 50 ppb lead, water B contains 30 ppb of lead and water C contains 10 ppb lead. A blend of 0.2 Ml of A, 0.1 Ml of B, and a volume of C, has a lead content of 20 ppb. What was the volume of C?

4. Shady Spring wishes to blend water A, lead content 50 ppb, with water C, lead content 10 ppb, to satisfy a lead content of less than or equal to 20 ppb. The company can only bottle 1 Ml of water. The sale price of the blend is 10 monetary units per Ml. The cost of A and C is 2 MU and 4 MU per Ml respectively. The objective is to maximise profit.

(a) Use a graphical method to identify the feasible region. Find the coordinates of the vertices of the feasible region.

(b) Calculate the profit at the the two vertices that are not at the origin.