Question $2(25$pts$)$: TOGG has a demand of $1750$ units$/$month of a certain SUV model and manufactures these cars in its own factory. The unit cost is $40000TL$ and the cost of preparing and making production setup for the order has been estimated to be $12000$TL$.$ The interest rate for capital is $20\%$ yearly. TOGG's manufacturing capacity is $42000$ units$/$year$.$

a$)$ What is the optimal order quantity to be produced?

b$)$ What is the number of production runs per year? Calculate the maximum inventory level?

c$)$ What is the sum of average annual cost of holding and setup?

d$)$ There is a supplier that provides battery for TOGG. Demand for battery is variable and the following weekly data is obtained from the last $52$ weeks. Cost of each full battery is $2500$TL and it sells for $3500TL.$ If the battery is unsold at the end of the week, it is recharged at a cost of $300TL.$ What is the optimal order quantity for the battery?

$\backslash$table$[[$Demand$($units$),1000,1250,1500,1750,2000,2250,2500,2750,3000,3250,3500],[\backslash$table$[[$Frequency$],[($number of observations$],[$out of $52$ weeks$)]],2,3,5,10,8,6,6,4,3,3,2]]$