He wants the total area to be 30 square meters. The fencing material he has chosen costs $5 per meter. What is the cheapest the fencing materials can cost?

Question

Bubba wants to grow watermelons and kumquats in separate fenced areas in his backyard. He decides to make one large, fenced area with a divider that is parallel to two sides. He wants the total area to be 30 square meters. The fencing material he has chosen costs $5 per meter. What is the cheapest the fencing materials can cost?

Answer 1

30 = 2l + 3w

30 - 3w = 2l

15 - 1.5w = l

A = lw

A = w(15 - 1.5w)

A = 15w - 1.5w²

Maximum at w = -15 / 2(-1.5)

That is w = 5, and l = 7.5