Question

Silver scooter finds that it costs $100 to produce each scooter and the fixed costs are $1000. the price is given by p=500-2x, where p is the price in dollars at which exactly x scooters will be sold. find the quantity of scooters that the company should produce and the price it should charge to maximize profit. find the maximum profit.

How many scooters should the company produce to maximize profit?

Answer 1

To maximize profit, the company should produce 4 scooters and charge $492 each. The maximum profit will be $200.

Step-by-step explanation:

To determine the profit-maximizing quantity of scooters the company should produce, we need to find the quantity where marginal cost (MC) is equal to marginal revenue (MR). Marginal cost is the change in total cost divided by the change in quantity, while marginal revenue is the change in total revenue divided by the change in quantity. Let's calculate the total revenue, marginal revenue, total cost, and marginal cost for different output levels:

QuantityTotal RevenueMarginal RevenueTotal CostMarginal Cost00-$1,000-1$400$400$1,100$1002$800$400$1,200$1003$1,200$400$1,300$1004$1,600$400$1,400$1005$2,000$400$1,500$100

From the table, we can see that the profit-maximizing quantity is 4 scooters, where MC = MR. The price the company should charge can be found by substituting the quantity into the price equation: p = 500 - 2x. So, p = 500 - 2(4) = 500 - 8 = $492.

To find the maximum profit, we can calculate the profit by subtracting the total cost from the total revenue at the profit-maximizing quantity. Profit = Total Revenue - Total Cost = $1,600 - $1,400 = $200.