A startup company can sell 1000 computers if they price them at $500. The number sold will increase by 10 for every $1 decrease in the price. The company has fixed costs of $100,000, and each computer costs 4300 To produce. find the price that will maximize the company's profit. How many computers will they sell at this price?

To find the price that will maximize the company's profit, we need to create a profit function and then determine the price that will make it reach its maximum value. Let's go step by step:

1. Determine the number of computers sold at a given price:
- We know that the company can sell 1000 computers if they price them at $500.
- We also know that the number sold will increase by 10 for every $1 decrease in price.

Let's denote the number of computers sold as 'x' and the price per computer as 'p'.

If the price per computer is $500, the number sold will be 1000.
Therefore, we can write the equation: x = 1000 + (500 - p) / 1 * 10.

2. Calculate the revenue:
- Revenue (R) is the product of the price per computer and the number of computers sold.
R = p * x.

3. Calculate the total cost:
- Each computer costs $4300 to produce.
- The fixed costs of the company are $100,000.
- Therefore, the total cost (C) is the sum of the cost to produce each computer and the fixed costs.
C = $4300 * x + $100,000.

4. Calculate the profit:
- Profit (P) is the difference between revenue and total cost.
P = R - C.

Substituting the expressions for revenue (step 2) and total cost (step 3) into the equation for profit (step 4), we get:
P = (p * x) - ($4300 * x + $100,000).

Now, we have a profit function in terms of the price per computer (p) and the number of computers sold (x). To find the price that maximizes profit, we can take the derivative of the profit function with respect to p and set it equal to zero. Then solve for p.

However, we need the specific values, such as the production cost ($4300) and the starting price ($500), to calculate the optimal price and the number of computers sold. Could you please provide these values?

To find the price that will maximize the company's profit, we need to determine the relationship between the price of the computers and the number of computers sold, as well as the total revenue and total cost.

Let's start by defining some variables:
- Let P be the price of a computer.
- Let N be the number of computers sold.
- Let R be the total revenue.
- Let TC be the total cost.
- Let F be the fixed costs.
- Let VC be the variable costs per unit.

From the given information, we know that the number of computers sold, N, will increase by 10 for every $1 decrease in the price, P. This can be represented as:

N = 1000 + 10 * (500 - P)

We also know that the cost to produce each computer is $4300, so the variable cost per unit, VC, is 4300.

The total revenue, R, can be calculated as the product of the price and the number of computers sold:

R = P * N

The total cost, TC, is the sum of the fixed costs, F, and the variable costs, which can be represented as:

TC = F + VC * N

The profit, Pr, is equal to the total revenue minus the total cost:

Pr = R - TC

Now, let's substitute the expressions we derived earlier into the profit equation:

Pr = (P * N) - (F + VC * N)
Pr = (P * (1000 + 10 * (500 - P))) - (F + 4300 * (1000 + 10 * (500 - P)))
Pr = (P * (1000 + 10 * 500 - 10P)) - (F + 4300 * (1000 + 10 * 500 - 10P))
Pr = (P * (1000 + 5000 - 10P)) - (F + 4300000 + 43000 * 500 - 43000 * 10P)
Pr = (P * (6000 - 10P)) - (F + 4300000 + 21500000 - 430000 * P)

To maximize profit, we need to find the price that will make the derivative of the profit equation equal to zero. Let's calculate the derivative of the profit equation with respect to P:

d(Pr)/dP = 6000 - 20P - 430000 + 43000
d(Pr)/dP = -20P - 426940

Setting the derivative equal to zero:

-20P - 426940 = 0
-20P = 426940
P = 426940 / -20
P = -21347

Since the price cannot be negative, it means there is no price that would maximize profit in this scenario.

However, we can calculate the profit and number of computers sold at the price of $500.

Substituting P = 500 into the profit equation:

Pr = (500 * (1000 + 10 * (500 - 500))) - (100000 + 4300 * (1000 + 10 * (500 - 500)))
Pr = (500 * 1000) - (100000 + 4300 * 1000)
Pr = 500000 - (100000 + 4300000)
Pr = 500000 - 4400000
Pr = -3900000

Since the profit is negative, it means that the company will experience a loss if they sell the computers at $500. Therefore, they should reconsider their pricing strategy.