Based on your previous analysis, the marketing office is proposing that the company produces cloth bags as a new product. Each bag requires 15 minutes of labor, 0.3 meters of cloth, and 0.01 pounds of crafting materials for each unit produced. What must the bags sell for so that they are profitable?

The company Crafting S.L located in California produces cloth, yarn, and crafting materials. So far they have only sold their products in the state but now they have decided to start selling their goods to other states. Since sales in California have not been very good lately, the goal of the company is maximizing their weekly profit from sales to other states and not sell in California anymore. The profit is computed as the difference between the revenue from sales and the cost of materials. The marketing office has done some research and got to the conclusion that they could sell all that they produce at $30 per meter of cloth, $9 per skein of yarn, and $25 per pound of crafting materials. In order to produce one meter of cloth, it is necessary to use 1 skein of yarn, 0.1 pounds of crafting materials and 200 yards of sewing thread (the company buys thread at $0.5 per 100 yards). Other necessary materials and expenses, such as machinery, cost about $4 per meter of cloth. In addition, it takes 30min. of labor to produce 1 meter of cloth. The company can produce a maximum of 5,500 meters of cloth per week. In order to produce 1 skein of yarn, the company uses 100 yards of sewing thread, 0.05 pounds of crafting materials, as well as, 5min. of labor. Additionally, the cost of the necessary machinery is about $2.5 per skein of yarn. The company can produce a maximum of 3,000 skeins of yarn per week. To produce one pound of crafting materials, the company uses 50min. of labor and the cost of the machinery used is $1.5 per pound. Additionally, they use 0.75 skeins of yarn and 0.12 meters of cloth. The maximum amount. of crafting materials that the company can produce is 500 pounds per week. The company has a maximum of 2000 hrs of labor available each week. And since it does not have a warehouse, everything that is produced needs to be sold or used to produce other goods. The company has credit to buy thread and simple crafting materials to produce cloth and yarn at a reduced price of $10 per pound at zero interest. But the company cannot buy more than 1000 pounds of simple crafting materials per week. The CEO of the company has hired you to lead their research team. The following are the tasks that you will have to accomplish with the help of your team