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Bob is planning to start an IT business, servicing computers that are infected with viruses. To start his new enterprise, Bob
estimates that he will need to spend $5,000 on equipment $6,000 on premises, $4,000 on advertising. All of these costs
are fixed. He is planning on charging his customers $250 each to fix an infected computer. For each computer that he fixes,
he must spend $25 on parts and software.
Suppose we let a be the number of computers that Bob fixes. How many computers does he need to fix to break even?
Give your answer to the nearest integer.

Respuesta :

Answer:

Step-by-step explanation:To determine the break-even point, we need to find the number of computers Bob needs to fix to cover his fixed costs.

Let's denote the fixed costs as:

Equipment cost = $5,000

Premises cost = $6,000

Advertising cost = $4,000

Total fixed costs = $5,000 + $6,000 + $4,000 = $15,000

Now, let's find the contribution margin per computer, which is the selling price per computer minus the variable cost per computer:

Selling price per computer = $250

Variable cost per computer = $25

Contribution margin per computer = $250 - $25 = $225

Now, we can find the break-even point (the number of computers Bob needs to fix to cover his fixed costs) using the formula:

Break-even point = Total fixed costs / Contribution margin per computer

Break-even point = $15,000 / $225 ≈ 66.67

Since we can't fix a fraction of a computer, Bob needs to fix at least 67 computers to break even. Therefore, the answer is 67 computers (rounded to the nearest integer).

msm555

Answer:

67 computers

Step-by-step explanation:

To find the number of computers (a) that Bob needs to fix to break even, we can set up a break-even equation. The revenue generated by fixing (a) computers should be equal to the total cost incurred. The break-even equation is given by:

[tex]\sf \textsf{Revenue} = \textsf{Cost} [/tex]

The revenue from fixing (a) computers is the product of the number of computers fixed (a) and the charge per computer ($250):

[tex]\sf \textsf{Revenue} = 250a [/tex]

The total cost includes the fixed costs for equipment, premises, and advertising, as well as the variable costs for parts and software:

[tex]\sf \textsf{Cost} = \textsf{Fixed Costs} + \textsf{Variable Costs} [/tex]

[tex]\sf \textsf{Cost} = 5000 + 6000 + 4000 + (25a) [/tex]

Now, set the revenue equal to the cost and solve for (a):

[tex]\sf 250a = 5000 + 6000 + 4000 + 25a [/tex]

Combine like terms:

[tex]\sf 250a - 25a = 15000 [/tex]

[tex]\sf 225a = 15000 [/tex]

[tex]\sf a = \dfrac{15000}{225} [/tex]

[tex]\sf a = 66.666666667 [/tex]

Bob cannot fix a fraction of a computer, so he needs to round up to the nearest whole number.

Therefore, Bob needs to fix approximately 67 computers to break even.

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