Math Project. Deals with profit. I really need help by Thursday 10/29 by 11:59am

[powerglare]

1. A company determines that the profit from selling ? units of an item is given by ?(?) = 0.0003?^2 + 5?. Find the marginal profit for 40 units sold and interpret its meaning in the context of the problem.

2. A small business has 200 scooters to rent If ? scooters are rented, the monthly profit is ?(?) = −5?^2 + 1800? − 60000. How many scooters need to be rented to maximize profit?

3. A company sells 1500 items per month at a price of $15 each. It is predicted that the monthly sales will increase by 125 items for each $0.30 reduction in price. Find the demand function. How many units must they sell to maximize revenue? What is the maximum revenue?

4. If the cost function is ?(?) = 3?^2 + 5? + 12, what is the minimum average cost?

 

[skeeter]

1. what is the definition of marginal profit and what does it mean?

2. how may one find the maximum value of a quadratic function, with or without using calculus?

3. Revenue = (number of units rented)(rental price)

let x be the number of 30 cent reductions ...

[MATH]R = (1500 + 125x)(15 - 0.30x)[/MATH]
... another quadratic function to maximize.

4. Believe you'll need to use calculus for this one ...

[MATH]C_{avg} = \dfrac{C(q)}{q}[/MATH]