Question

urijah is starting a catering business the cost to start is 50000 and the monthly costs are 8000.he has been earning 10800 every month in revene in how many mounths will his business break even and earn profit

Answer 1

18 months

Explanation:

We can determine in how many months will Urijah break-even using the cost and revenue functions.

For a business to break even, their revenue must equal their cost:

Break-even: revenue = cost

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Cost function:

The cost function is the sum of the variable costs (i.e., marginal cost * quantity) and the fixed cost:

Cost = (marginal cost * quantity) + fixed cost

Algebraically, the cost function is given by:

C(q) = mq + b, where

• C is the cost per q items produced,
• mq is the marginal cost (i.e., increase in cost per additional items made),
• and b is the fixed costs.

Determining whether each cost is the marginal cost or the fixed cost:

Now we can start defining the 50000 and 8000 costs:

• Since it costs 50000 to start the catering business, this is our fixed cost as it would cost this much, even if there were no monthly costs.
• Since it costs 8000 each month to run the business, it's our marginal cost, as cost increases by 8000 each month.

Cost function in context of the problem:

Thus, the cost function for this problem is given by:

C(q) = 8000q + 50000

Revenue function:

The revenue function is the product of price and quantity:

Revenue = price * quantity:

Algebraically, the revenue function is given by:

R(q) = pq, where

• R is the revenue per q items sold,
• p is the price of the item,
• and q is the quantity of items sold.

Determining which value is the price:

• Since Urijah earns 10800 every month, its the price.

Revenue function in context of the problem:

Thus, the revenue function is given by:

R(q) = 10800q

Determine in how many months will Urijah break even:

Now we can determine in how many months will Urijah break even by setting R(q) equal to C(q) and solving for q:

R(q) = C(q)

(10800q = 8000q + 50000) - 8000q

(2800q = 50000) / 2800q

q = 17.85714286

• We need to round to the nearest whole number, meaning q = 18.

Thus, it will take 18 months for Urijah to break-even and earn a profit