Peter Danson who owns a herd of 100 dairy cattle. Peter's dairy farm is very successful, partially due to the diet he feeds his herd. Each head of cattle receives a minimum of 100 units of calcium, 20,000 calories, and 1500 units of protein. Peter gives his herd Star Cow Feed. Each ounce costs $0.015 and provides 1 unit of calcium, 400 calories, and 20 units of protein Peter has recently been approached by Michael Mause, Vaca, a feed for dairy cattle. Each ounce of Una Vaca costs $0.020 and provides 2 units of calcium, 250 calories, and 20 units of protein salesman marketing Una (a) Explain why Michael Mause could not convince Peter to switch his herd to use only the Una Vaca feed (b) Suppose Michael offers to provide a special blend of Star Cow and Una Vaca just for Peter's herd. This mixture would meet Peter's minimum nutrition require- ments at minimum cost. However, Michael says that in order for his company to earn a profit, the price per head of cattle for the mix must be greater than or equal to $1.00. Formulate a linear programming model to determine how many ounces of each feed type should be in the special mix (c) Graphically solve the model you created in part (b). List the extreme points and their corresponding objective values. Describe the optimal solution in words. Would Peter be willing to switch from Star Cow Feed to this special mix? Explain (d) A constraint is redundant if its removal does not change the shape of the feasible region. Does this problem have any redundant constraints? Explain Peter Danson who owns a herd of 100 dairy cattle. Peter's dairy farm is very successful, partially due to the diet he feeds his herd. Each head of cattle receives a minimum of 100 units of calcium, 20,000 calories, and 1500 units of protein. Peter gives his herd Star Cow Feed. Each ounce costs $0.015 and provides 1 unit of calcium, 400 calories, and 20 units of protein Peter has recently been approached by Michael Mause, Vaca, a feed for dairy cattle. Each ounce of Una Vaca costs $0.020 and provides 2 units of calcium, 250 calories, and 20 units of protein salesman marketing Una (a) Explain why Michael Mause could not convince Peter to switch his herd to use only the Una Vaca feed (b) Suppose Michael offers to provide a special blend of Star Cow and Una Vaca just for Peter's herd. This mixture would meet Peter's minimum nutrition require- ments at minimum cost. However, Michael says that in order for his company to earn a profit, the price per head of cattle for the mix must be greater than or equal to $1.00. Formulate a linear programming model to determine how many ounces of each feed type should be in the special mix (c) Graphically solve the model you created in part (b). List the extreme points and their corresponding objective values. Describe the optimal solution in words. Would Peter be willing to switch from Star Cow Feed to this special mix? Explain (d) A constraint is redundant if its removal does not change the shape of the feasible region. Does this problem have any redundant constraints? Explain
