Answer:
The Expected cosy of the builder is $433.3
Step-by-step explanation:
$400 is the fixed cost due to delay.
Given Y ~ U(1,4).
Calculating the Variable Cost, V
V = $0 if Y≤ 2
V = 50(Y-2) if Y > 2
This can be summarised to
V = 50 max(0,Y)
Cost = 400 + 50 max(0, Y-2)
Expected Value is then calculated by;
Waiting day =2
Additional day = at least 1
Total = 3
E(max,{0, Y - 2}) = integral of Max {0, y - 2} * ⅓ Lower bound = 1; Upper bound = 4, (4,1)
Reducing the integration to lowest term
E(max,{0, Y - 2}) = integral of (y - 2) * ⅓ dy Lower bound = 2; Upper bound = 4 (4,2)
E(max,{0, Y - 2}) = integral of (y) * ⅓ dy Lower bound = 0; Upper bound = 2 (2,0)
Integrating, we have
y²/6 (2,0)
= (2²-0²)/6
= 4/6 = ⅔
Cost = 400 + 50 max(0, Y-2)
Cost = 400 + 50 * ⅔
Cost = 400 + 33.3
Cost = 433.3
= (2/3)x - 6