Problem 1:

Define the parameters and variables and write the equation for the following scenario to optimize the profit:

A factory has forecast demand for each of their 2 products for the next 12 month which they may meet but cannot exceed. They currently have 50 employees who are on salary ($4000/month), that is they have to be paid whether they are producing product or not. There are 160 productive hours per worker in a month. Overtime is on an hourly basis and costs $40/hour. Maximum overtime per employee per month is 30 hours. Employees may be hired ($6,000 each), but not laid off during this year. The selling price of the two products is $85 and $15 respectively. The amount of time required to produce each product is 2 hours and 0.5 hours respectively. Ignore material and overhead costs. Inventory carrying costs are $2 and $0.25 per month respectively. Shortages are not allowed. Initial Inventories are zero.

Problem 2:

Define the parameters and variables and write the equation for the following scenario to optimize the profit:

A factory has forecast demand for each of their 2 products for the next 12 month which they may meet but cannot exceed. They currently have 100 employees who are on salary ($3900/month), that is they have to be paid whether they are producing product or not. There are 160 productive hours per worker in a month. Overtime is on an hourly basis and costs $38/hour. Maximum overtime per employee per month is 35 hours. Employees may be hired ($4,000 each), but not laid off during this year. The selling price of the two products is $180 and $30 respectively. The amount of time required to produce each product is 4 hours and 1.5 hours respectively. Ignore material and overhead costs. Inventory carrying costs are $4 and $0.50 per month respectively. Shortages are not allowed. Initial Inventories are zero.