A company that manufactures bicycles has a fixed cost of $100,000 for equipment and facilities. It cost $100 in parts and labor to produce each bicycle. The bicycles will sell for $300 each. Find the number of bicycles needed to be sold in order for the company to have a gain.
Could someone explain how to find this?
A club can buy shirts for $14.50 each. Alternately, it can make the shirts by buying plain T-Shirts for $6.25 each, fabric paint for $32.75, and a pack of stencils for $8.50. For how many shirts is making the T-shirts cost the same as buying the shirts?
And this?
cost for x bikes is 100,000 + 100x
income from x bikes is 300x
To have a gain, income > cost
So, you need
300x > 100,000 + 100x
200x > 100,000
x > 500
Check: for 501 bikes, cost is 150100, revenue is 150300, so a gin
For 499 bikes, cost is 149,900 and revenue is 149700, so a loss
See what you can do with the other one.
I need help to get better understaning on how to create 1 variable equations
I am confused on the other one But I know to try and use the information given so here is my try.
6.25+32.75+8.50 = 14.50T
I used T as the variable
Did I do it right oobleck
To find the number of bicycles needed to be sold in order for the company to have a gain, we can use the concept of break-even analysis.
First, let's calculate the total cost per bicycle. We have the fixed cost, which is $100,000 for equipment and facilities. Additionally, it costs $100 in parts and labor to produce each bicycle. Therefore, the total cost per bicycle is $100,000 + $100 = $100,100.
Next, let's calculate the profit per bicycle. The selling price is $300 each, and the cost per bicycle is $100,100. So, the profit per bicycle is $300 - $100,100 = -$99,800.
To determine the number of bicycles needed to cover the fixed cost and start making a gain, we divide the fixed cost by the profit per bicycle: $100,000 / -$99,800.
However, it's important to note that a negative profit indicates a loss, not a gain. In this case, the company needs to sell more bicycles than the obtained result to start making a profit. The actual number of bicycles required to have a gain will depend on factors such as demand, competition, and other expenses.
For your second question about calculating the number of shirts at which making T-shirts costs the same as buying them, we can set up an equation:
Let's assume the number of shirts needed is x.
For buying the shirts, the cost per shirt is $14.50.
For making the shirts, we need to add the costs of plain T-shirts, fabric paint, and stencils. The cost of plain T-shirts is $6.25 per shirt, fabric paint is $32.75, and the pack of stencils is $8.50.
Therefore, the total cost per shirt when making the T-shirts is 6.25 + 32.75/x + 8.50/x.
Now we can set up the equation:
14.50 = 6.25 + 32.75/x + 8.50/x
To solve this equation, we can combine like terms and bring all the terms to one side:
14.50 - 6.25 = 32.75/x + 8.50/x
8.25 = (32.75 + 8.50) / x
8.25 = 41.25 / x
Cross-multiplying:
8.25x = 41.25
Dividing both sides by 8.25:
x = 5
Therefore, making the T-shirts will cost the same as buying them when producing 5 shirts.