A barbershop has the following demand for haircuts on Saturday, which is its busiest day of the week.

Number of Haircuts Probability

$200\mathrm{.}1$

$250\mathrm{.}3$

$300\mathrm{.}4$

$350\mathrm{.}1$

$400\mathrm{.}1$

a$.$ What is the average demand for haircuts on Saturday?

b$.$ If the capacity is $35$ haircuts, what is the average utilization of the shop? $($Enter answer as a percent and round to $3$ decimal places.$)$

c$.$ If capacity is $35$ haircuts, how much of a capacity cushion does it have?

d$.$ If it costs $$50$ per lost haircut due to customer dissatisfaction and $$100$ for each unit of capacity provided, how much capacity should be built to minimize costs?