XYZ Ltd produces three products, X $,$Y and Z$.$ The capacity of XYZ Ltd$\text{'}$s plant is restricted by process alpha. Process alpha is expected to be operational for eight hours per day and can produce $1,200$ units of X per hour,$1,500$ units of Y per hour, and $600$ units of Z per hour.

Selling prices and material costs for each product are as follows.

Product Selling price Material cost

K per unit K per unit

X $15080$

Y $12040$

Z $300100$

Conversion costs are K$720,000$ per day.

Required:

$($a$)$ Calculate the profit per day if daily output achieved is $6,000$ units of X$,4,500$ units of Y and $1,200$ units of Z

$($b$)$ Calculate the TA ration for each product.

$($c$)$ In the asbsence of demand restrictions for the three products, advise management on the optimal production plan.

$($d$)$ Distinguish between throughput accounting and limiting factor analysis