linear programming question

Question

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.

Answer 1

Goal: Maximize profit (p) from sales of study tables (x) and computer tables (y). p = 100x + 160y

I will assume semiskilled and unskilled are equivalent. For the skilled workers, the total amount of hours is 6(38). These skilled workers can build a study table in 2 hours (2x) and a computer table in 2 hours (2y). Therefore, 2x + 2y ≤ 6(38). For the unskilled workers, the total amount of hours is 11(38). These unskilled workers can build a study table in 2 hours (2x) and a computer table in 5 hours (5y). Therefore, 2x + 5y ≤ 11(38). Assume x and y have to be greater than or equal to 0. Use bolded equations/statements for your linear program.