Question

Iced tea, x, costs $4 per gallon and lemonade, y, costs $6 per gallon. You need to purchase at least 9 gallons of drinks for a neighborhood picnic, but have at most $55 to spend. Model the scenario with a system of inequalities. Which of the following options represents a possible solution to the system of inequalities?

Answer 1

Solution:

To find the inequalities which give a solution space to the problem, we consider the variable x for iced and the variable y for lemonade, where x ≥ 0 and y ≥ 0

Then the inequalities are

x + y ≥ 9 ..... (1)

4x + 6y ≤ 55 ..... (2)

x ≥ 0 ..... (3)

y ≥ 0 ..... (4)

We can construct the given graph by taking (1), (2), (3) and (4) no. inequalities as equations. However the required solution space is given by the bounded region in the first quadrant.

Remark:

If there was any objective function given, we could formulate an L.P.P. and solve it for a maximization or minimization problem.