PLEASE show all work and explain each step so that I can learn the process. Thanks!

A manufacturing company has a small plant where they make three different products. All products use welding, paint and final assembly. Product A requires 15 minutes on welding, 8 minutes on paint and 12 minutes on assembly. Product B requires 12 minutes on welding, 15 minutes on paint and 9 minutes on assembly. Product C is not painted and requires 20 minutes on welding and 10 minutes on assembly. Assume that the firm runs two shifts and has 920 minutes available per day on each resource. The firm estimates maximum daily demand to be 50 for A, 60 for B and 50 for C. Assume the firm can sell each A for $1000, each B for $1200 and each C for $800. Assume that resource costs and labor in the plant are fixed costs and that the firm would like to maximize the profits it makes by manufacturing the three products in the plant.

1. Formulate the problem of maximizing the daily profits as a linear program. Let A, B and C denote the number of each type of product the firm will make.

2. The firm is considering paying either the welding, paint or assembly operators extra money to schedule overtime. Each hour of overtime costs $50 fully loaded. Conceptually describe how you would decide whether overtime should be scheduled on any of the three processes (welding, paint or assembly) by evaluating the linear programming output.