Craft Studio Furnishings (CSF) produces a unique line of cane furniture. The items currently on the market are table chairs, easy chairs, and love seats. The studio is considering introducing two new products: coffee tables and end tables, and is seeking to optimize their weekly production plan by means of a linear optimization model.

The productions of any item consist of manufacturing a wooden frame, stretching the woven cane onto the frame, and finishing. Each procedure is performed by a different shop at the studio. Labor utilization by each product and hours of labor available in each shop are shown in the table below. The contribution to earnings of each product is also shown.

In addition to the resource constraints mentioned above, CSF wishes to limit the production of the new products to no more than 10 units each pear week.

a) Formulate the above problem as linear optimization model.

b) Solve the problem using Excel.

c) What are the binding constraints and the non-binding constraints?

d) Why is the shadow price of the stretching constraints zero?

e) What is the economic interpretation of each of the shadow prices, for each of the constraints in the model?

Table Easy Love Coffee End Chair Chair Seat Availability Table (hours) Table Frame Manufacturing (hours) 1.3 0.5 0.5 40 Stretching (hours) 1.2 1.5 2 1.5 80 Finishing (hours) 1.5 1.7 60 Contribution to Earnings ($/unit) 30 44 57 55 45 1.