A grocery store must decide on the shelf space to be allocated to each of five types of breakfast cereals. The maximum daily demand is 100, 85, 140, 80, and 90 boxes, respectively. The shelf space in square inches for the respective boxes is 16, 24, 18, 22, and 20. The total available shelf space is 5,000 in^2. The profit per unit is $1, $2, $3, $2, and $4, respectively. (a) Model the problem of finding the store's greatest profit as an LP. (b) Solve the model in (a). Consider the dictionary of a maximization LP below: z = 0 + 22x_1 - 93x_2 - 21 x_2 - 21x_3 + 24x_3 x_4 = 0 - 1/2 x_1 + 3/2 x_2 + 1/2 x_3 - x_6 x_3 = 0 + 4x_1 - 8x_2 - 2x_3 + 9x_6 x_7 = 1 - x_1. which is degenerate. Therefore, potentially, Simplex may cycle. Starting from this dictionary, solve the LP with Bland's rule. Give the phase 1 LP of the following linear programming problem: minimize z = 2x_1 + 5x_2 + 6x_3 s.t. 2x_1 + 6x_2 + 3x_3 greaterthanorequalto 12 3x_1 + x_2 + 7x_3 = 11 x_1, x_2, x_3 greaterthanorequalto 0. A grocery store must decide on the shelf space to be allocated to each of five types of breakfast cereals. The maximum daily demand is 100, 85, 140, 80, and 90 boxes, respectively. The shelf space in square inches for the respective boxes is 16, 24, 18, 22, and 20. The total available shelf space is 5,000 in^2. The profit per unit is $1, $2, $3, $2, and $4, respectively. (a) Model the problem of finding the store's greatest profit as an LP. (b) Solve the model in (a). Consider the dictionary of a maximization LP below: z = 0 + 22x_1 - 93x_2 - 21 x_2 - 21x_3 + 24x_3 x_4 = 0 - 1/2 x_1 + 3/2 x_2 + 1/2 x_3 - x_6 x_3 = 0 + 4x_1 - 8x_2 - 2x_3 + 9x_6 x_7 = 1 - x_1. which is degenerate. Therefore, potentially, Simplex may cycle. Starting from this dictionary, solve the LP with Bland's rule. Give the phase 1 LP of the following linear programming problem: minimize z = 2x_1 + 5x_2 + 6x_3 s.t. 2x_1 + 6x_2 + 3x_3 greaterthanorequalto 12 3x_1 + x_2 + 7x_3 = 11 x_1, x_2, x_3 greaterthanorequalto 0