LİNEAR PROGRAMMİNG PROBLEM

Question

1. A furniture manufacturer employs 6 skilled and 11 semiskilled workers and produces two products: study table and computer table. A study table requires 2 h of a skilled worker and 2 h of an unskilled worker. A computer table requires 2 h of a skilled worker and 5 h of an unskilled worker. As per the industrial laws, no one is allowed to work for more than 38 h a week. The manufacturer can sell as many tables as he can produce. If the profit for a study table is $100 and for a computer table $160, how many study and computer tables should the manufacturer produce in a week in order to maximize the overall profit? Formulate a linear programming model.

2. Consider Problem 1 in Exercises. Suppose that the demands of the study and computer tables are at least 40 and 45, respectively, and the manufacturer pays $900 and $600 per week for each skilled and unskilled worker, respectively. If the manufacturer intends to fulfill the demand in full, what objective function would you suggest to the manufacturer’s production planning problem? Justify your suggestion and formulate the problem as a linear programming model.

3. Consider Problems 1 and 2 in Exercises. Suppose the manufacturer is interested in maximizing his overall profit rather than fulfilling the demand. What objective function would you suggest to the manufacturer’s production planning problem? Justify your suggestion and formulate the problem as a linear programming model.

Answer 1

Re; #1 6 skilled worker @ max 38 hrs/wk = 228 hrs available.

11 semi-skilled @ 38 hrs/wk = 418 hrs available.

Study tables need 2 hrs skilled, so can make max 114 tables; need 2 hrs semi-skilled, so can make a max of

418/2 = 209 tables. So qty is limited to 114 study tables/wk max. If made only study tables and no computer tables, profit would be 114 x $100/table = $11,400

Computer tables need 2hrs skilled, and 5 hrs unskilled. Doing similar calc'n as above, they are limited to make a maximum of 83 computer tables if made no study tables. Profit is 83 x $160/table = $13,280

Any combination of both types would lead to a profit somewhere in between these two values. My suggestion would be to make just computer tables. I would like to see a response that uses true linear programming techniques. Is my logic valid?