Question: just answer third picture question, thank you ! Smith Manufacturing produces two popular grades of commercial carpeting among its many other products. In the coming
just answer third picture question, thank you !
Smith Manufacturing produces two popular grades of commercial carpeting among its many other products. In the coming production period, Smith needs to decide how many rolls of each grade should be produced in order to maximize profit. Each roll of Grade X carpet uses 50 units of synthetic liber. requires 25 hours of production time, and needs 20 units of foam backing. Each roll of Grade y carpet uses 40 units of synthetic fiber. requires 28 hours of production time, and needs 15 units of foam backing. The cost to Smith of one unit of synthetic fiber is $2. Smith also pays $1.50 for each unit of foam backing, and one hour of production time costs $50. The list price Smith quotes its customers is $1755.56 per roll or Grade X carpet and $1.847.22 per roll or Grade Y carpet . Smith offers all its customers a 10 percent discount off the list price. In the coming production period, Smith has 3000 units of synthetic fiber available for use. Workers have been scheduled to provide at least 1800 hours of production time (overtime is a possibility). The company has 1500 units of foam backing available for use 2. The union representing Smith's factory workers has decided that the workers will not work more than 1800 hours in the coming production period. How does this affect the feasible region and the extreme points? Has the optimal solution and the profit changed? 3. Smith's management has increased the discount to the list price for Grade X carpet to 12 percent. Using the feasible region defined in Part 2 above, does this change the optimal solution and the maximum profit? VALUE OF OBJECTIVE FUNCTION AT ALL EXTREME POINTS


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