Let's begin by constructing a cost formula for this process.

• Total Cost = (Cost of Bags per Batch + Cost of Labor per Batch + Cost of Oil per Batch) x Batches

Having established our cost formula, let's evaluate each scenario:

(a) Determine the cost of preparing one batch of 100 pieces.

We see that 10 bags would be required (100 pieces per batch / 10 pieces per bag) at a price of $3 per bag. Additionally, preparing a batch of 100 pieces requires 2 hours of work at a wage rate of $8 per hour. Finally, one unit of fresh oil will be necessary at a cost of $5 per batch. Plugging in these figures to our cost formula, we'll solve.

• Total Cost = (Cost of Bags per Batch + Cost of Labor per Batch + Cost of Oil per Batch) x Batches
• Total Cost = (($3 per bag x 10 bags per batch) + ($8 per hour x 2 hours per batch) + ($5 per unit x 1 unit per batch)) x 1 batch
• Total Cost = ($30 per batch + $16 per batch + $5 per batch) x 1 batch
• Total Cost = ($51 per batch) x 1 batch
• Total Cost = $51

(b) If management projects that it will sell 300 pieces of fried chicken determine the total batch and unit costs.

Using the same cost formula from above, adjusting the batch number to 3 (3 batches of 100), we'll solve for the total batch cost.

• Total Cost = (Cost of Bags per Batch + Cost of Labor per Batch + Cost of Oil per Batch) x Batches
• Total Cost = (($3 per bag x 10 bags per batch) + ($8 per hour x 2 hours per batch) + ($5 per unit x 1 unit per batch)) x 3 batches
• Total Cost = ($30 per batch + $16 per batch + $5 per batch) x 3 batches
• Total Cost = ($51 per batch) x 3 batches
• Total Cost = $153

Dividing this total cost by the total number of units, we'll solve for the unit cost.

• Unit Cost = Total Cost / Total Units
• Unit Cost = $153 / 300 units
• Unit Cost = $0.51 per unit

(c) If management estimates the sales to be 250 pieces, determine the total costs.

We are told that each batch "must be 100 pieces." Thus, even though the company only expects to sell 250 pieces, batches must be completed in multiples of 100. This means that 3 batches must be completed to produce the 250 units demanded. As calculated in part (b), the total cost of 3 batches is equal to $153.

(d) How much will the batch costs increase if the government raises the minimum wage to $10 per hour?

Returning to our cost formula, let's adjust for the minimum wage increase.

• Total Cost = Cost of Bags per Batch + Cost of Labor per Batch + Cost of Oil per Batch
• Total Cost per Batch = ($3 per bag x 10 bags per batch) + ($10 per hour x 2 hours per batch) + ($5 per unit x 1 unit per batch)
• Total Cost per Batch = ($30 per batch) + ($20 per batch) + ($5 per batch)
• Total Cost per Batch = $55 per batch

We see that the total cost per batch will increase by $4 ($55 - $51).

(e) If management decided to reduce the number of pieces in a batch to 50, determine the cost of preparing 250 pieces. Assume that the batch would take half as long to prepare, and management wants to replace the oil after 50 pieces are cooked.

First, let's adjust our cost formula for these changes. Note that bags will be reduced to 5 (50 pieces per batch / 10 pieces per bag), and hours will be cut in half from 2 to 1. Since management wants to replace the oil after 50 pieces are cooked, the units of oil per batch remains equal to 1 unit per batch.

• Total Cost = (Cost of Bags per Batch + Cost of Labor per Batch + Cost of Oil per Batch) x Batches
• Total Cost = (($3 per bag x 5 bags per batch) + ($8 per hour x 1 hours per batch) + ($5 per unit x 1 unit per batch)) x (250 pieces / 50 pieces per batch)
• Total Cost = (($15 per batch) + ($8 per batch) + ($5 per batch)) x 5 batches
• Total Cost = $28 per batch x 5 batches
• Total Cost = $140