Gusto Gardens, a large plant nursery, grows and sells rare tropical plants. The operators find that when they grow fewer plants of a certain type, customers pay more for that type of plant. If they grow q Red Mambo plants, they can charge 390–3q dollars for each one, which means their revenue will be q(390–3q) dollars. They have to pay $30 for fertilizer and water to grow each Red Mambo plant, plus an additional $6,000 in other expenses. This means that their costs will be 30q+6,000 dollars. So, if they grow q Red Mambos, their profit in dollars will be q(390–3q)–(30q+6,000).
This expression can be simplified to –3q2+360q–6,000 and then written in factored form as –3(q–20)(q–100).
What do the numbers 20 and 100 represent in the expression?
