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Page 1 > of 5 0 - ZOOM + A concrete company mixes two ingredients, A and B, and packages the resulting concrete mix into 50 th hags Each Ib of ingredieat A costs 5.15 and contains 37 lb of tine sand, 33 lb of coarse sand, and 30 lb of gravel. Each tb of ingredient B costs $.18 and contains 50 th of fine sand, 35 lb of coarse sand, and 15 lb of gravel. There are three specifications regarding the content of a concrete bag in terms of fine sand, coarse sand and gravel and their relationship f concrete mix must contain at least 18 but no more than 26 lbs of fine sand, at least 10 lbs of coarse sand, and at least 8 but no more than 15 lbs of gravel. A fourth specification stipulates that the ratio of the lbs of fine sand in a bag to the lbs of coarse sand in a bag should be at least 1 to 3. (a) The company desires to know the combination (in lbs) of ingredients A and B to fill a 50 lbs bag that matrizes the total materials cost. Formulate a linear programming model for this problern (define variables and write the objective function and constraints. Do not solve. (b) The optimal solutions sur vots to mix 16.13 lbs of ingredient A and 33.87 lbs of ingredient B to make a 50 lb bag of concrete with the least materials cast, while satisfying all specifications. (1) How many lbs of fine sand, care sand and gravel will be contained in the optimal mix of the 50 lb hag? (in) Which specifications are satisfied at their lower or upper bounds (2) Up to now, the company was making 50 lbs bags of concrete by mixing 10 lbs of (equivalently, which specification constraints are binding? ingredient A and 40 lbs of ingredient B. (it) Were the four specifications satisfied? (iv) How much money the company will save per bag if it pursues the optimal solution Page 1 > of 5 0 - ZOOM + A concrete company mixes two ingredients, A and B, and packages the resulting concrete mix into 50 th hags Each Ib of ingredieat A costs 5.15 and contains 37 lb of tine sand, 33 lb of coarse sand, and 30 lb of gravel. Each tb of ingredient B costs $.18 and contains 50 th of fine sand, 35 lb of coarse sand, and 15 lb of gravel. There are three specifications regarding the content of a concrete bag in terms of fine sand, coarse sand and gravel and their relationship f concrete mix must contain at least 18 but no more than 26 lbs of fine sand, at least 10 lbs of coarse sand, and at least 8 but no more than 15 lbs of gravel. A fourth specification stipulates that the ratio of the lbs of fine sand in a bag to the lbs of coarse sand in a bag should be at least 1 to 3. (a) The company desires to know the combination (in lbs) of ingredients A and B to fill a 50 lbs bag that matrizes the total materials cost. Formulate a linear programming model for this problern (define variables and write the objective function and constraints. Do not solve. (b) The optimal solutions sur vots to mix 16.13 lbs of ingredient A and 33.87 lbs of ingredient B to make a 50 lb bag of concrete with the least materials cast, while satisfying all specifications. (1) How many lbs of fine sand, care sand and gravel will be contained in the optimal mix of the 50 lb hag? (in) Which specifications are satisfied at their lower or upper bounds (2) Up to now, the company was making 50 lbs bags of concrete by mixing 10 lbs of (equivalently, which specification constraints are binding? ingredient A and 40 lbs of ingredient B. (it) Were the four specifications satisfied? (iv) How much money the company will save per bag if it pursues the optimal solution