A company is planning to produce and sell a new line of tvs. The fixed cost for the company is $400,440 and each tv cost $845 to produce. If they project the sales price of 1200, how many tvs will need to be sold to break even? If they decide to reduce the price to 1199.99, how many additional tvs will they need to sell to break even?

$400,440 + 845x =1200x

$400,440 + 845x = 1199.99x

x = # of TVs

to get the answer to the second part compare your answer from the 1st to the 2nd.

$400,440 + 845x =1200x

$400,440 + 845x = 1199.99x

To determine the number of TVs needed to break even, we need to calculate the total cost and compare it with the revenue generated from sales.

1. Initially, let's calculate the break-even quantity when the sales price is projected at $1200:
- Fixed costs: $400,440
- Cost per TV: $845
- Sales price per TV: $1200

To break even, the total revenue generated must cover the fixed costs plus the variable costs. Variable costs consist of the cost per TV multiplied by the number of TVs sold.

Let's denote the break-even quantity as 'x':
Total cost = Fixed cost + (Cost per TV * x)
Total revenue = Sales price per TV * x

To break even, the total revenue must equal the total cost:
Total revenue = Total cost

So we can set up the equation:
Sales price per TV * x = Fixed cost + (Cost per TV * x)

Now we can solve for 'x':
1200 * x = 400,440 + (845 * x)
1200x - 845x = 400,440
355x = 400,440
x = 400,440 / 355
x ≈ 1127.66

To break even, the company would need to sell approximately 1128 TVs at a sales price of $1200.

2. Now let's calculate the additional TVs needed to break even at a reduced sales price of $1199.99:
- Sales price per TV: $1199.99

Follow the same process as before:
Total revenue = Sales price per TV * x
Total revenue = Total cost

1199.99 * x = 400,440 + (845 * x)
1199.99x - 845x = 400,440
354.99x = 400,440
x = 400,440 / 354.99
x ≈ 1129.83

To break even at a sales price of $1199.99, the company will need to sell approximately 1129 additional TVs beyond the initial 1128 TVs sold at $1200 each.