Question

Frank owns a clothing store that sells shorts and graphic T-shirts. He sells the shorts for $14 each and the T-shirts for $6 each. He is limited to the constraints shown by the set of inequalities below.

s≤ 18-0.5
s≥ 10-t
s≤ 30-t
s≥ 0
t≥ 0
Which of the points (s,t) will maximize Frank's revenue?
a. (0,30)
b. (18,0)
c. (6,24)
d. (0,10)

Answer 1

To maximize revenue, we evaluate the given points and calculate the revenue for each. The point (18,0) generates the highest revenue of $252.

Step-by-step explanation:

To maximize Frank's revenue, we need to find the point (s,t) that satisfies all the given constraints and generates the highest value of revenue R, where R = 14s + 6t.

Let's check each of the given points to see if they satisfy all the constraints and calculate their corresponding revenue:

• Point (0,30): This point satisfies all the constraints, and the revenue is R = 14(0) + 6(30) = $180.
• Point (18,0): This point satisfies all the constraints, and the revenue is R = 14(18) + 6(0) = $252.
• Point (6,24): This point satisfies all the constraints, and the revenue is R = 14(6) + 6(24) = $192.
• Point (0,10): This point satisfies all the constraints, and the revenue is R = 14(0) + 6(10) = $60.

Out of these points, the point (18,0) generates the highest revenue of $252. Therefore, the correct answer is (b) (18,0).