Question

When the admission price for a baseball game was $4 per ticket, 54,000 tickets were sold. When the price was raised to $5, only 48,000 tickets were sold. Assume that the demand function is linear and that the variable and fixed costs for the ball park owners are $0.10 and $95,000 respectively. (a) Find the profit P as a function of x, the number of tickets sold. P(x) = (b) Select the graph of P. y 150000 150000 150000 100000 100000F 1000001 50000 50000 50000 x 20000 40000 60000 20000 40000 60000 20000 40000 60000 -50000 -50000 -50000 -100000 -100000 -1000000 0-150000 00-150000 -150000 O 0 150000 100000 50000 20000 40000 60000 -50000 -1000001 o-150000 0

Answer 1

solution: fu raised to 45 Step (: 54,000 tckets u8,000 tickets $0.10 $ 95,000 at pi antb when x = 50,000 Pau 1 54000 a + b = 4 p=5, when adooo a +b=5 Xe 448,000 =) 6000 a 1 Q = 6000 if ac- then 6000 shooo -6000 t b=4 be 13 Hence, + 13 6000 2 R = px + 13n 6000 fixed Cost F (n) 95,000 cca)95,000 + $(0-10)* profit fonchon peale R(x)-C(2) peale +13x - 95000 - (0.10) 22 6000 2 t 6000 } (x) a (12.9)x - 95000 Now the related graph is ③

for marginal profit :p'(x) p'(x) = of a C - x² +12.9)x - 95000 p'(x) = - 2x Since of a x² na +12.9, 1 6ooo Υ p'(x) = +12.9 3000 q -87000 2ooo +12.9 if x = 27,000, then p'(21,000): = 3.9 per ticket if x=50,000, then p'(54,000) = -54,000 +12.9 3000 = -18 12.9 i - 5.1