Sweatshirts at the school store cost $30. They currently sell about 4 shirts per month. They have decided to decrease the price
of the shirts. They found the for each each $1.50 decrease, they will sell 2 more shirts per month. How many decreases in prices will give the max value? A. 30
A club usually sells 1200 shirts a year at $20 each. A survey indicates that for every $2 increase in price, there will be a drop of 60 sales a year. What price they should charge for each shirt to maximize the revenue? : Let x = no. of $2 increases also Let x = no. 60 shirt sales reductions : Price = (20 + 2x) No. of shirts = (1200 - 60x) : Revenue = price * no. of shirts sold, therefore: R = (20 + 2x)*(1200 - 60x) FOIL R = 24000 - 1200x + 2400x - 120x^2 Arranges as a quadratic equation R = -120x^2 + 1200x + 24000 Find the axis of symmetry to find the price for max revenue: x = -b/(2a) In this equation; a=-120; b=1200 x = %28-1200%29%2F%282%2A-120%29 x = %28-1200%29%2F%28-240%29 x = +5 ea $2 increases and 5*60 = 300 reduction in shirt sales: : Price for max sales; 20 +2(5) = $30, will sell 1200 - 300 = 900 shirts : Max revenue: 30 * 900 = $27,000
