A product engineer at a midsize electronic manufacturing firm located in Chicago must decide how many computers to produce next month. The firm is planning to produce three types of computers: laptops, desktops and commercial servers.

The product engineer knows that laptops typically yield an average profit of $500, desktops typically yield an average profit of $400 and servers typically yield and average of $650. He also knows that laptops, desktops and servers cost $400, $350 and 500$ respectively to produce and that no more than $70,000 is available for production next month.

Based on market research, the firm would like to obtain a production of at least 20 units of each type of computers, but no more than 25 servers and no more than 40 desktops. Due to the popularity of laptops, the firm would like to produce at least twice as many laptops than desktops and servers combined.

a. Formulate algebraically a linear programming model for this manufacturing problem that maximizes profits based on given constraints.

b) Determine the optimal solution and the maximum profit and include “a managerial statement” that communicates the results of the analyses (i.e. describe verbally the results).

c) Using the answer report determine the amount of slack for the budget constraint of $70,000. Include the answer report and briefly explain your answer.