11 a B1 3 B1 for a clearly graph drawn B Minimum demand = 1 M1 M1 for method of solving equation when demand = 1 So 1 = 45 000 175P – This graph shows expected sales for the 175P = 44 999 different prices charged. If he prices his = P snowboard at more than £257 demand will = £257 be 0. A1 A1 for answer £257 The graph also shows that the cheaper the snowboards, the more he will sell. But he needs to consider his charges to make sense of it all. B1 B1 for a clear explanation Number sold = 450 00 175P – P Sales = number sold × = (45 000 175P)P – B2 B1 for explaining the relationship b Costs = set-up fees + manufacturing costs B1 for commenting that there will be other costs to take per board into account Demand = 45 000 + 95P c M1 M1 for setting up the sales equation Profit = sales costs – M1 M1 for setting up the profit equation Profit = (45 000 175P)P – (45 000 + 95P) – = 45 000P 175P2 45 000 95P – – – = 44 905P 175P2 45 000 – – A1 A1 for cao d From a graph of this quadratic B2 B1 for profit between £2 800 000 and £2 900 000 function, his maximum profit would be B1 for cost of boards between £120 and £140 approximately £2 850 000 if he sold his boards at £135. B1 B1 for a drawn graph of the quadratic equation found
11 a b c d This graph shows expected sales for the different prices charged. If he prices his snowboard at more than £257 demand will be 0. The graph also shows that the cheaper the snowboards, the more he will sell. But he needs to consider his charges to make sense of it all. Number sold = 450 00 – 175P Sales = number sold × P = (45 000 – 175P)P Costs = set-up fees + manufacturing costs per board Minimum demand = 1 So 1 = 45 000 – 175P 175P = 44 999 P = = £257 Demand = 45 000 + 95P Profit = sales – costs Profit = (45 000 – 175P)P – (45 000 + 95P) = 45 000P – 175P2 – 45 000 – 95P = 44 905P – 175P2 – 45 000 From a graph of this quadratic function, his maximum profit would be approximately £2 850 000 if he sold his boards at £135. B1 M1 A1 B1 B2 M1 M1 A1 B2 B1 3 B1 for a clearly graph drawn M1 for method of solving equation when demand = 1 A1 for answer £257 B1 for a clear explanation B1 for explaining the relationship B1 for commenting that there will be other costs to take into account M1 for setting up the sales equation M1 for setting up the profit equation A1 for cao B1 for profit between £2 800 000 and £2 900 000 B1 for cost of boards between £120 and £140 B1 for a drawn graph of the quadratic equation found B
Higher_Skills_Algebra_MarkScheme_AQA.docx