On wednesday may 22, ms. christy cheung, owner of the yarn barn asked the staff members of question: on wednesday may 22, ms. christy cheung, owner of the yarn barn asked the staff members of her on wednesday may 22, ms. christy cheung, owner of the yarn barn asked the staff members of her company to meet with her and her determine the amount of yarn products to produce for the upcoming season. the yarn barn is a small business operating in the hintonburg neighbourhood of ottawa and, as a mill, they specialize in producing yarn products on site and selling them to local yarn shops in the area. strands of yarn are made from various types of fibers (e. g., cotton or wool). the yarn barn receives shipment from their supplier in the form of blended fibers (typea and type b) and workers at the yarn barn twist the blended fibers to form yarn, the final product that is used and sold. the fiber order purchased last month, was beginning to arrive and operations to make yarn will have to start by the following tuesday to meet customer demands in time. during the meeting, jennifer underhill, who is responsible for placing orders, noted that the latest shipment from suppliers will be 3000 kg, and of that 20% will be type a fiber while the rest is type b fiber. the yarn barn sells their final products in skeins and each skein consists of 200 g of yarn, made from a combination of the type a and type b fibers. christy asked jennifer about the demand from clients for the upcoming season and jennifer believes that with the growing popularity of knitting and sustainable fashion in general, they’ll be able to sell everything they produce. jennifer prepared a report of the yarn barn’s anticipated selling price for the three products they’ll produce (shown in figure 1). these selling prices are set based on the company’s long-term marketing strategy and the forecasted demand. selling price per skein grade 1 $6.00 grade 2 $7.50 grade 3 $10.00 figure 1: selling price for yarn barn products looking at the report, christy believes they’ll do quite well this season. the yarn barn has a new accounting system in place, and she was able to calculate the contribution of each product they’re going to sell and the incremental profit on a skein of grade 3 yarn is greater than the incremental profit on other grades. christy had calculated the yarn product’s contributions when the finer shipment was purchased back in february at an average cost of 2 cents per gram. jennifer brought to christy’s attention that despite the profit contribution being more for grade 3, it was impossible to produce only grade 3 yarn because there’s not enough type a fiber in the shipment. the yarn barn can make three grades of yarn to be sold and their quality is judged on the percentage of wool in the products. type a fiber has 90% wool and type b has 50%. the minimum average quality of grade 3 yarn requires 80% wool. grade 2 yarn requires at least 60% wool. grade 1 yarn is made entirely from type b fiber. jennifer explained that because only 20% of the 3000 kg shipment is type a, their production of grade 3 yarn is limited by this. christy argued that it’s not really a limitation because another supplier recently approached her and offered her 80 kg of type a fiber for 5 cents per gram. she turned down the offer at the time but believes it’s still available if they want to pursue it. 1. formulate the linear programming model that can be used to the yarn barn decide the optimal production policy for this coming season. christy wants to know how many skeins to produce and what each grade’s composition should be to maximize revenue. disregard christy’s suggestion of buying 80 kg of type a fiber from another supplier for now