May 2019 Q7 a.

Joycarpap Ltd manufactures and sells three models of affordable toys: Car, Joy and Pap. Each model requires specific amount of fabrication, material worth and assembly hours, as shown in the table below:

There are 210 fabrication hours available and 170 hours of assembly. Materials in stock are worth GH¢200. Market research conducted by the company revealed that demand for the toys was such that in whatever combination of the three models produced, all of the output can be sold within a week.
Each Car contributes GH¢15 to profit, each Joy contributes GH¢20 to profit and each Pap contributes GH¢14 to profit. Using, as slack variables and P as total profit,
Required:
i) Formulate a linear programming problem.                                                                                                                      (4 marks)

ii) Set up the initial Simplex Tableau.                                                                                                                                 (4 marks)

iii) Determine the total profit in the first iteration.                                                                                                              (5 marks)