Question: A small manufacturer produces parts for the auto industry. For a particular part, the fixed costs which include setting up the machines are $1250. The material and labor costs are $9.50 per part. The owners of the factory charge $13.05 for each part. Suppose \[x\] denotes the number of brochures produced and sold. Find the following.

a) A linear function which calculates the cost of producing \[x\] parts.

b) A linear function which calculates the revenue realized from the sale of \[x\] parts.

c) Use a) and b) to find the linear profit function for this product

d) What is the profit or loss realized from the sale of 425 parts?

e) What is the break-even point for this product?

f) Suppose an aircraft manufacturer wants a discount on an order of 375 parts. What must the part manufacturer charge at a minimum to break even on an order of 375 parts?