Consider a small pharmacy where two pharmacists, one drive$-$thru assistant and one cashier work.

$$ On average, $60\%$ of the customers come to fill prescriptions, $30\%$ purchase only over the counter $($OTC$)$ medication, and $10\%$ for both. Assume that each customer drops one script at a time.

$$ Customers who come in to fill a prescription drop their script with the cashier. This step takes on average $3$ minutes per customer.

$$ After spending $5$ minutes on a script, the pharmacist realizes that $10\%$ of the scripts are problematic and cannot be filled as is$.$ For those scripts, the pharmacist calls the insurer and$/$or the doctor$$s office to resolve the problems. Problem resolution and eventually filling the script takes on average an additional $45$ minutes. Assume that all problematic scripts are eventually filled.

$$ The remaining unproblematic scripts take an additional $10$ minutes for the pharmacist to fill after the $5-$minute review.

$$ All customers pay the cashier. Check$-$out is on average $5$ minutes per customer.

$30\%$ of the prescription customers pick up their order at the drive thru. This step is carried out by the drive thru assistant and takes $6$ minutes.

a$.$ Compute the capacities of the pharmacists, drive$-$thru assistant, and the cashier in customers per hour.

b$.$ Seeing that the drive$-$thru assistant$$s utilization is so low, the pharmacy decides to merge the cashier and drive$-$thru positions such that a team of two employees handle the tasks carried out by the cashier and the drive$-$thru assistant. Does this process redesign affect the overall capacity of the pharmacy? Please justify your answer by using the relevant capacity calculations.