Cox Electric makes electronic components and has estimated the following for a new design of one of its products: Fixed Cost = $10,000 Material cost per unit = $0.15 Labor cost per unit = $0.10 Revenue per unit = $0.65 Note that fixed cost is incurred regardless of the amount produced. Per unit material and labor costs together make up the variable cost per unit. Assuming Cox Electric sells all that it produces; profit is calculated by subtracting the fixed cost and total variable cost from total revenue.

Question:

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Cox Electric makes electronic components and has estimated the following for a new design of one of its products: Fixed Cost = $10,000 Material cost per unit = $0.15 Labor cost per unit = $0.10 Revenue per unit = $0.65 Note that fixed cost is incurred regardless of the amount produced. Per unit material and labor costs together make up the variable cost per unit. Assuming Cox Electric sells all that it produces; profit is calculated by subtracting the fixed cost and total variable cost from total revenue.

a) Give a mathematical model for computing profit

b) If Cox Electric produces 120, 000 units of the new product, calculate the resulting profit

a) P = 0.4Q  - 10,000

b) $38,000

Explanation:

Profit is the difference  between the total revenue from a product and the total cost. Total cost is the sum of fixed cost plus variable cost. It can also be determined as the difference between total contribution and the fixed cost.

Contribution is the difference sales revenue and variable cost

a) Mathematical model for profit

Therefore, a model for calculating profit can be estimated as follows:

Profit = (Selling price - unit variable cost ) × unit - Fixed cost

Variable cost = 0.15+0.10 = $0.25

Selling price = $0.65

Selling price -unit variable cost  = 0.65 - 0.25 = 0.4

Model:

P = 0.4Q  - 10,000

Where Q- quantity sold, S- selling price, V- unit variable cost , P = profit

Note that this model assumes that unit variable cost, selling price and total fixed cost are constant through all activity levels.

b) The resulting profit from the sales of 120,000 units

Using this model, we can work out the profit as follows:

Profit = 0.4Q - 10,000

Q- 120,000

Profit = ( 0.4× 120,000)- 10,000

       = $38,000

what

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