Joe\'s Coffee Shoppe orders fresh doughnuts each morning. Joe pays $3.20 per dozen doughnuts and sell doughnuts for $0.4 each. The leftover doughnuts are salvaged at half the selling price. Suppose that the demand for doughnuts is uniformly distributed from 16 dozens to 30 dozens. How many doughnuts (in dozens) should Joe stock each day? A detailed analysis of past data shows that the number of doughnuts sold per day is better described by a normal distribution, with a mean 23 dozens and standard deviation 10 dozens. Now, how many doughnuts should Joe stock each day? The expected demand was the same in parts (a) and (b), but the optimal order quantities should have been different. What accounted for this different. What accounted for this difference? Solution.

1. List the transformations to the basic graph and then graph the function f(x)=3 (+7)^2-5
Solution
The list of transformations to the basic graph are
(i) Translation
(ii) Shifting
(iii) Scale (Streching / Compression), and
(iv) Reflections
The given fnctio is f(x) = 3 (+7)^2 - 5 = 3 x 49 - 5 = 142
Which is a constant graph. Thus, the graph is parallel to x-axis and at a distance 142 units above
the x - axis.