A steel company must decide how to allocate its weekly time on a rolling mill. The mill takes
unfinished slabs of steel as input and can produce two semi-finished products: bands and
coils. The mill’s two products come off the rolling line at different rates and have different
profitabilities. To further complicate matters, weekly production amounts must be limited to not exceed maximum demands. The following data is available. Tons per hour Profit per ton Maximum tons Bands 200 £25 6000 Coils 140 £30 4000 The question now facing the company is as follows: If 40 hours of production time are available each week, how many tons of bands and coils should be produced to maximise profit?
a) Formulate this problem as a linear programme. Clearly define your decision variables
b) Solve the problem using the graphical method.
c) Write the simplex tableau for the optimal solution obtained in part b.
d) By how much can each of the profitabilities change for the optimal solution to stay
the same? Every ton of bands produced results in 90 kg of waste and every ton of coils gives 200 kg of waste. A new policy is adopted to restrict waste to 810000 kg. Add this new constraint and using your solution in part c resolve the resulting linear programme
using dual simplex.
