Dakota Furniture Company makes handmade artistic wooden furniture for aesthetic enhancement of living rooms in old houses. During upcoming production period South Dakota Furniture Company is planning to make Chairs, Dressers, and Tables respectively. The time required for each product to go through the three stages of production (cutting, finishing and assembly in minutes) are the resources in this problem. The unit profit for chair, dresser and table are $90, $50, and $20 respectively.

Furthermore, the amount of each resource needed to produce chair, dresser and table and the total amount of resource available during the production period is as follows. Each chair requires 40 minutes of cutting, 50 minutes of finishing and 80 minutes of assembly. Each dresser requires 10 minutes of cutting, 20 minutes of finishing and 10 minutes of assembly. Each table requires 15 minutes of cutting, 50 minutes of finishing and 10 minutes of assembly. Based on available labor and machines, the manufacturing plant during the production period has 2000 minutes of cutting time, 3000 minutes of finishing time, and 1000 minutes of assembly time.

1. Formulate and solve a linear programming model to determine the production levels that would maximize profit.
2. Does your LP Model have multiple optimal solutions?

Solve this using excel and show you descision variables and contraints?