A firm produces three products X,Y and Z. Each product is produced by means of four operations, "heating", "mixing", "cooling" and "setting". These operations are all in limited supply. Resource usage (per kg of each product produced) is as follows: Resource constraints are as follows: - Heating: 110 kilogramme-hours per month available - Mixing: 1,200 kilogramme-hours per month available - Cooling: 2,000 kilogramme-hours per month available - Setting: Setting takes place in a dedicated setting room. The setting room can hold 50kg at a time of products X,Y and Z, and is available for use for 54 hours each month. Contributions to profit per kg for each product are estimated at: Required: a) Formulate the above problem as a linear programming problem. You are not required to solve the problem. The firm's production manager has obtained a computer printout of the final simplex tableau for this problem, a summary of which is provided below. In this tableau, X,Y and Z represent the three products, and the variables S1,S2 and S3 are slack variables representing unused resources for heating, mixing and setting respectively. Final Tableau: Required: b) Suggest why the "cooling" constraint has been omitted from this tableau, and state the shadow price of cooling time. c) Interpret fully the final tableau, and suggest ways in which this information may be utilised by the firm. In your interpretation, emphasis should be given to the economically significant components of the tableau. d) "The appropriate use of linear programming in business decision-making depends crucially on the assumptions underlying the linear programming decision model." Explain these assumptions and discuss the extent to which they are likely to be satisfied in a practical business setting