You are an operations manager for a company called ZA Fabrics, a manufacturer of two types of fabrics, Linen and Silk, in Johannesburg. The company is currently planning its production schedule for the next month and needs to determine how many units of Linen and Silk it should produce to maximize profit. The profit per meter of Linen is R30, and for Silk, it is R50. The company has 4000 hours of labour available per month and a maximum capacity of 20000 meters of fabric. Each meter of Linen requires 2 hours of labour, while each meter of Silk requires 1 hour.

Given these constraints, answer the following questions:
1. Formulate this problem as a linear programming problem. Clearly state the objective function and the constraints. (5)
2. Define the concept of shadow pricing and discuss potential limitations or challenges of using shadow pricing. (5)
a.  Contract costing is an essential technique used in managerial accounting to track costs and determine profitability in projects.
b.  Discuss the concept of contract costing and its features. Identify and describe the different types of contracts commonly encountered in contract costing. (5)
c.  Furthermore, analyse the advantages and disadvantages of contracts from the perspectives of both manufacturers and contractees.