TMA Company produces three products; Standard, Deluxe and Luxury in three of its departments which are Cutting, Assembly and Finishing. The total available labour hours per week for Cutting, Assembly and Finishing departments are 180, 300 and 240 respectively.
To produce two units of Standard requires 240 minutes in the Cutting department, half the amount of time in the Assembly department and same amount of time in the Finishing department as in the Cutting department.
To produce one unit of Deluxe requires 60 minutes, 180 minutes and 60 minutes in Cutting, Assembly and Finishing departments respectively.
To produce three units of Luxury requires 180 minutes in Cutting department and twice the amount of time in both Assembly and Finishing departments.
The contribution per unit from Standard, Deluxe and Luxury is Sh.6, Sh.5 and Sh.2 per unit respectively.
Required:
(i)Formulate the above problem as a linear programming model.(6 marks)
(ii)Prepare an initial simplex tableau to solve the above model.(4 marks)