A cabinet company produces cabinets used in mobile and motor homes. Cabinets produced for motor homes are smaller and made from less expensive materials than those for mobile homes. The home office in Dayton Ohio has just distributed to its individual manufacturing centres the production quotas required during the upcoming quarter. The scheduled production requirements for the Huber Heights OHOI plant are provided in the table below.
Each motor home cabinet requires three man hours to produce whereas each mobile home cabinet requires five man hours. Labor rates normally average $18 pr hour. During July and august however when the company employs many part time workers labor rates only average $14 and $16 per hours respectively. A total of 2.100 man hours are available in July 1,500 in august and 1,200 in September. During any given month management can schedule up to 50% additional man hours using overtime as the standard rate of time and a half. Material costs of motor home cabinets are $146andfor mobile home cabinets they are $210.
The plant expects to have 25 motor home an d20 mobile home assembled cabinets in stock at the beginning of July. The home office wants the plant to have at least 10 motor home and 25 mobile cabinet assemblies in stocks at the beginning of October to cover possible shortages in production at the other plants.
The plants has storage facilities capable of holding up to 300 cabinets in any one month. The costs for storing motor home cabinets is $6 pr cabinet and $9 for storing mobile home cabinets per cabinet.
Formulate a linear programming model to help management devise a monthly production schedule for the next quarter that will minimize their costs over the quarter. Report back the production and storage levels. Report costs per month in addition to the total costs.
Implement your formulation in excel and fin d the optimal solution using solver. Summarize your solution (decision variable values and objective functions value ) below your formulation. Report back the production and storage levels. Report costs per month in addition to the total costs.