A manufacturing store 40 laptops per week at a per week at the prize of $200 each. The manager estimates that for each $25 prize reduction she can sell 5 more laptops per week. The laptops cost the store $30 each, if x stands for the number of $25 prize reductions. a.) Find the prize function p(x) and the quantity function q(x) b.) Find the revenue R(x) and the cost function C(x) c.) Sketch the profit function. d.) Find the value of x that maximizes profit. [3marks] e.) Plot the graph of R(x) and c(x) on a single graph paper and indicate the break even point and comment on the production. [8marks] f.) Find the average rate of change (ARC) profit.