SOLUTION: Woods Limited manufactures and sells x small patio tables each day. The daily cost of production is modeled as C(x) = 3x2 + 1500, and the revenue produced each day is modeled as R(
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Question 959010: Woods Limited manufactures and sells x small patio tables each day. The daily cost of production is modeled as C(x) = 3x2 + 1500, and the revenue produced each day is modeled as R(x) = 180x. Suppose the company is limited by time to producing at least 30 tables every day. What is the break-even point? If the company sells 45 tables, then what is the profit? How many tables must the company produce in order to get a profit of $1,125? What happen if the company produces 58 tables?
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
Woods Limited manufactures and sells small patio tables each day.
The daily cost of production is modeled as
, and the revenue produced each day is modeled as .
Suppose the company is limited by time to producing at least (at least means ≥)tables every day.
1. What is the break-even point?
to find it set , then solve the resulting quadratic equation
he break-even point occurs when
.......simplify, divide all terms by
........use quadratic formula
solutions:
or
your solution is because the company is producing at least tables to have the break-even point ; so, disregard
2. If the company sells tables, then what is the profit?
The profit function ,
write in terms of , then evaluate
=> the profit the company earns if sells tables
3.
How many tables must the company produce in order to get a profit of $?
Set , then solve the resulting quadratic equation
........use quadratic formula
we need only positive value since represents an order
- exact solution
round it to whole number since represents tables
4.
What happen if the company produces tables?
evaluate
=> the profit the company earns if sells tables
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