Question: A furniture manufacturer produces three products, desks, tables, and chairs. These products can be produced during either the morning shift or the evening shift. The morning shift has a labor cost of $20 per hour with a maximum availability of 20,000 hours. The evening shift has a labor cost of $25 per hour and is limited to 15,000 hours. The labor, lumber, and demand requirements are given as follows:

Resource Desk Table Chair

Labor (hours) 0.75 2 0.5

Lumber (pounds) 7 15 4

Nails (pounds) 0.5 2 0.25

Demand: 50 75 100

Assume that there are 20,000 pounds of lumber and 20,000 pounds of nails available for both shifts.

Formulate this problem to minimize total labor cost.