Question

Sandra's Sweaters' production function is shown in the above table. Sandra rents three knitting machines for $30 a day each and hires workers at a wage rate of $40 a day. If Sandra produces18 sweaters per day, what is her average total cost?

Answer 1

The average total cost (ATC) is calculated by dividing the total costs by the quantity of output, which in Sandra's case, would need the exact number of workers she hires to be accurate. Assuming one worker, the ATC for producing 18 sweaters with the cost of machines and one worker's wage would be approximately $7.22 per sweater.

Step-by-step explanation:

You're looking to calculate Sandra's average total cost (ATC) for producing 18 sweaters a day. The ATC is found by dividing her total costs by the number of sweaters she produces. You've mentioned she rents three knitting machines at $30 each per day and hires workers at $40 a day.

Firstly, we'll need to determine the total cost of renting the machines and hiring the workers. If we assume that she needs to hire a certain number of workers to produce the 18 sweaters, that number should be specified to calculate the labor costs accurately.

However, without the specific number of workers, we can only provide the calculation for the machines:

• Cost of renting machines per day = 3 machines × $30/machine = $90

Let's assume she hires one worker (as we're not provided with the actual number of workers):

• Labor cost per day = 1 worker × $40/worker = $40

Now we add the cost of machines and labor to find the total daily cost:

• Total daily cost = cost of machines + labor cost = $90 + $40 = $130

Finally, the average total cost of producing 18 sweaters is:

• ATC = Total daily cost / Quantity of output = $130 / 18 sweaters = approximately $7.22 per sweater

Remember, to get the accurate ATC, you would need the exact number of workers Sandra employs to produce the 18 sweaters.

Answer 2

To calculate the average total cost, consider both the fixed costs and the variable costs. In this case, the fixed costs are the rent for the knitting machines, and the variable costs are the wages paid to the workers. By plugging in the values and using the formula, the average total cost is calculated to be $96.67.

Step-by-step explanation:

To calculate the average total cost, we need to consider both the fixed costs and the variable costs. In this case, the fixed costs are the rent for the knitting machines, which is $30 per day for each machine, totaling $90 per day. The variable costs are the wages paid to the workers, which is $40 per day for each worker. Given that Sandra produces 18 sweaters per day, we can calculate the average total cost as follows:

Fixed Costs + (Variable Costs / Quantity) = Average Total Cost

$90 + (3 * $40 / 18) = Average Total Cost

$90 + $120 / 18 = Average Total Cost

$90 + $6.67 = Average Total Cost

Average Total Cost = $96.67