A toy shop sells watercolour sets made up from different components. The Hunior set has 3 brushes and 6 colour tablets with a pack of 20 sheets of art paper, the Senior set has 5 brushes and 15 colour tablets with a pack of 20 sheets of art paper, while the Deluxe set has 8 brushes, 20 colour tablets and 30 sheets of art paper.The shop presently has 250 brushes, 600 colour tablets and 1400 sheets of art paper in stock.It makes profits of $5, $10 and $12 on the Junior, Senior and Deluxe sets respectively.
a) use the simplex algorithm to find out how many of each set the shop should make up to obtain maximum profit while coherently, concisely and logically justifying your procedures and decisions.
b) while getting the material out, a staff member finds another 100 brushes and 200 colour tablets in the stock room. Investigate and evaluate the change in maximum profit and identify any assumptions and their associated effects for the mathematical model. Refine your model in relation to the parameters of your results and analyse the results of your BFS to incorporate any associated effects of your refined model on the profit function.