Problems on Linear Programming

Problem 1: Rahim Factory manufactures two articles- share and towel. To manufacture share a certain machine has to be worked for 1.5 hours and in addition a craftsman has to work for two hours. To manufacture the towel the machine has to work for 2.5 hours, in addition the craftsman has to work for 1.5 hours. In a week, the factory can avail 80 hours of machine and 70 hours of craftsman. The profit on each share is Tk 50 that on each towel is TK 40.

If all the articles produced can be sold away, find how many of each kind i.e., share and towel should be produced to earn maximum profit per week. Formulate the model using linear programming model and solve it.

Problem 2: Mrs Saleha has learnt from a nutrition book that her family needs at least 330 gm of protein and 45 mg of iron per day. These nutrients can be obtained from meat and vegetables. Each pound of meat costs on an average of $1.6 and contains average of 150 gm. and 15 mg of iron, while each pound of vegetable costs 50 cents ($1/2) and has 10 gm. of protein and 5 mg of iron. Mrs. Saleha wants to determine the quantities of food that meet the nutritional requirements at least costs.