Solve Problem 9 graphically.
a. How many hours of the cutter’s time are used? Does it have any leftover time?
b. If the fitter is able to reduce the cost of product A from €8 to €6 and product B from €12 to €9, what will be the impact of cost reduction on the optimal answers?

c. If the fitter is able to use additional 50 hours (from 250 to 300) with the costs in Problem 9, what is the optimal product mix?

Data From Problem 9

A fitter produces two types of fitting products—product A and product B—using a cutting machine (cutter) and a grinding machine (grinder). Product A requires 4 hours of the cutter and 8 hours of the grinder; product B requires 6 hours of the cutter and 4 hours of the grinder. The cutter has processing hours of at most 300 hours and at least 200 hours. The grinder has maximum processing time of 250 hours. The cost involved in the production of product A is €8 and of product B is €12. The fitter expects that the combined production for products A and B must total at least 50 units. The fitter wants to determine the number of units of product A (x₁) and product B(x₂) that will minimize the cost of manufacturing.
a. Formulate a linear programming model for this problem.
b. Transform this model into a standard form.