Math

Linear Programming Solutions

Maximize P subject to the given constraints. P = 3x + 8y constraints x ≥ 0 y ≥ 0 x + y ≤ 2 a. P = 16 at (0, 2) b. P = 6 at (2,0) c. none of these d. P = 0 at (0,0) e. P = 22 at (3,8)

Maximize P subject to the given constraints. P= 14y – x constraints x ≤ 7 y ≥ 0 -x + 7y ≤ 6 x +y ≥ 5 a. none of these b. P = 26 at (13/7, 14) c. P = 19 at (7, 13/7) d. P = 70 at (0,5)

Maximize P subject to the given constraints. P = x – 10y constraints. x ≤ 10 y ≤ 4 x ≥ 0 y ≥ 0 x +y ≤ 14 a. P=26 at (10, 4) b. none of these c. P=14 at (14, 0) d. P=10 at (10, 0)

Minimize P subject to the given constraints. P= 9x + y constraints x ≥ 0 y ≥ 0 -x + 3y ≤ 8 -3x + y ≥ -3 a. P=0 at (0, 0) b. P=9 at (1, 0) c. P=-3 at (0, -3) d. none of these

Graph the inequality. 3x + y<5 Use the graphing tool to graph the inequality.

Graph the solution of the system of linear inequalities. 2x-3y ≤ 6 y≤ - 4 Use the graphing tool to graph the solution.

Graph the inequality. 4x+y<2 Use the graphing tool to graph the inequality.

Write a system of equations in two variables and solve. 1500 concert tickets were sold for a jazz festival. Tickets cost $25 for covered seats and $15 for lawn seats. Total receipts were $28,500. How many of each type of ticket were sold? System of equations: Number of tickets sold for covered seats: ___________. Number of tickets sold for lawn seats: ______________.

Sweet-Fit jeans has a factory that makes two styles of jeans; Super-Fit and Super-Hug. Each pair of Super-Fit takes 12 minutes to cut and 15 minutes to sew and finish. Each pair of Super-Hug takes 12 minutes to cut and 40 minutes to sew and finish. The plant has enough workers to provide at most 12,599 minutes per day for cutting and at most 28,249 minutes per day for sewing and finishing. The profit on each pair of Super-Fit is $6.50 and the profit on each pair of Super-Hug is $8.50. How many pairs of each style should be produced per day to obtain maximum profit? Find the maximum daily profit. (Use x for Super-Fit and y for Super-Hug.) Maximize P= 6.50 + 8.50y

Using the information below to create the initial simplex matrix. Assume all variables are nonnegative. Maximize f = 6x₁ +5x₂ + 7x₃ subject to 9x₁ + 7x₂ + 10x₃ ≤ 65 10x₁ + 3x₂ + 6x₃ ≤ 50 4x₁ + 10x₂ + 6x₃ ≤ 45 x₁ ≥0 x₂ ≥ 0 x₃ ≥ 0

Minimize P subject to the given constraints. P = 16x + 2y constraints x ≥ 0 y ≥ 0 x + 2y ≥ 8 2x + y ≥ 8 a. P =16 at (0, 8) b. P = 8 at (0, 2) c. P = -32 at (-2, 0) d. none of these

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