A unit manufactures 50,000 bottles of tomato ketchup in a year. The factory cost per bottle is Rs.6, the set-up cost per production run is estimated to be Rs.90 and the carrying cost on finished good inventory are 20% of the cost per annum. Production rate is 600 bottles per day and sales are expected at 150 bottles/day.
(i) Derive an expression for lot size that will give minimum cost.
(ii) What is the optimum lot size?
(iii) What is the numbers of runs required per year?
(iv) What will be the total cost per year if the number of runs has to be an integer?