A level Further Maths HelpWatch
Angelo manages a winter sports shop in a ski resort. He needs to decide how many snowboards and how many pairs of skis to purchase for the coming season to maximise his profit from hiring them out.
He has space for at most 250 snowboards and 500 pairs of skis.
Because there are more skiers than snowboarders Angelo will purchase at least 10% more pairs of skis than snowboards.
Both snowboards and skis need servicing, and his servicing facility can cope with no more than 600 units (ie snowboards or pairs of skis).
His expected profit from buying and renting out a snowboard is €40 for the season, and his expected profit from buying and renting out a pair of skis is €50 for the season.
(i) Define appropriate variables, construct inequality constraints, and draw a graph representing the feasible region for Angelo’s decision problem. 
(ii) Give the objective function and find the solution which will give the maximum profit. 
Angelo considers increasing the cost of snowboard hire so that snowboard profits rise enough to change the
(iii) By how much will snowboard profits have to rise to change the optimal solution? Angelo increases the cost of snowboard hire and creates extra storage space for snowboards. (iv) What is the greatest number of extra snowboards it is worth Angelo accommodating?