The beta container company is a large manufacturer in the container industry. the company's production factory enjoyed good employee relations, due to absence of frequent 'hiring-firing' practice. if necessary, the factory employed temporary workers and college graduates to fill extra manpower needs during the peak summer and monsoon months. the factory had 14 can lines, with 12 workers and 1 supervisor per line. the average shift hourly rate for workers and supervisors was 61 and 94 respectively. a 50% overtime premium was paid for all overtime work not exceeding 20 hours per worker per week (maximum 4 hours per day). the supervisor also received overtime on the same basis. the factory produced, stocked and transported cans in truckloads. each truckload occupied 3200 cubic feet of space. a monthly charge of 2% of the average monthly inventory value was applied to cover inventory carrying costs. the factory's average production capacity was 30 truckloads of cans/month/can line on regular time. the factory could use upto a maximum of 14 can lines in any month, if needed. the manufacturing cost was 50,000/truckload. table below shows the anticipated sales forecast. assume each can line works for 160 hours per month on regular time. table : anticipated sales forecast
month
demand in truckloads
january
30
february
54
march
145
april
186
may
217
june
262
july
317
august
346
september
299
october
251
november
101
december
119
: (a) how should the factory plan its production ?
(b) what will be the annual production plan that will result in least total annual cost using seven can lines in each month ?
(c) how will the production plan be affected if the factory had an initial inventory of 100 truckloads at the beginning of january ?
(d) how will the production plan be affected if the factory wanted an inventory of 150 truckloads at the end of december, but had no inventory at the start of january ?