Al Nakheel factory produces 3 different types of products. Product1: halva, product2: lokum, and product3: tahini. The annual demand for tahini is between 2000 and 2250 tons, for halva is between 600 and 750 tons and for lokum is between 250 and 300 tons. Product 1 and 2 require sesame as a raw material (M1) whereas for lokum the main raw material is jelly(M2). The raw material for products 1 and 2 arrive monthly per 400 tons, and it costs the company $1700 per ton of sesame. The raw material for product 3 also arrives monthly per 10 tons and it costs $250 per ton. The daily usage of raw material 1 is at least 1 ton per day and for raw material 2 is at most 700 kg. The minimum quantity that should be produced of both products 1 and 2 is 1.3 tons. Due to the company policy, there should always be an overproduction of the 3 products for new coming customers or orders or due to the delay in the raw materials from the supplier. The 3 products are stored in the same warehouse and each ton of product 1 product 2, and product 3 cost the company $43 as a holding cost.

Processing time for the different products per ton

Product1(halva)	Product2(tahini)	Product3(lokum)	Available hours for each machine (capacity)
Machine1	150 min	2126
Machine2	60 min	2250
Machine3	600 min	2250
Selling price/ton ($)	$4,000	$5,185.2	$3,333.3

Optimization is to maximize the profit of the company by using linear programming.

Answer rating: 100% (QA)

To formulate the linear programming problem lets define the decision variables Let x1 be the number ... View the full answer