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hart manufacturing makes three products. each product requires manufacturing operations in three departments: a, b, and c. the labor-hour requirements, by department, are as follows: during the next production period, the labor-hours available are 450 in department a, 350 in department b, and 50 in department c. the profit contributions per unit are $25 for product 1, $28 for product 2, and $30 for product 3. formulate a linear programming model for maximizing total profit contribution. if required, round your answers to two decimal places. for those boxes in which you must enter subtractive or negative numbers use a minus sign. (example: -300) let pi
hart manufacturing makes three products. each product requires manufacturing operations in three departments: a, b, and c. the labor-hour requirements, by department, are as follows: during the next production period, the labor-hours available are 450 in department a, 350 in department b, and 50 in department c. the profit contributions per unit are $25 for product 1, $28 for product 2, and $30 for product 3. formulate a linear programming model for maximizing total profit contribution. if required, round your answers to two decimal places. for those boxes in which you must enter subtractive or negative numbers use a minus sign. (example: -300) let pi
The linearprogramming modelfor maximizing totalprofitcontribution for all 3 departments is subject to X₁, X₂, X₃ ≥ 0.How to formulate linear programming?To formulate alinear programming modelfor maximizing total profit contribution forHartManufacturing, we can use the following variables:X₁ = number of units of product 1 producedX₂ = number of units of product 2 producedX₃ = number of units of product 3 producedThen, we can write the objective function as:Maximize Z = 25X₁ + 28X₂ + 30X₃Subject to the followingconstraints:Department A:Labor hours required for product 1 in department A = 2 hoursLabor hours required for product 2 in department A = 4 hoursLabor hours required for product 3 in department A = 3 hours2X₁ + 4X₂ + 3X₃ ≤ 450 (hours available in department A)Department B:Labor hours required for product 1 in department B = 3 hoursLabor hours required for product 2 in department B = 5 hoursLabor hours required for product 3 in department B = 2 hours3X₁ + 5X₂ + 2X₃ ≤ 350 (hours available in department B)Department C:Labor hours required for product 1 in department C = 1 hourLabor hours required for product 2 in department C = 1 hourLabor hours required for product 3 in department C = 3 hours1X₁ + 1X₂ + 3X₃ ≤ 50 (hours available in department C)Non-negativity constraints:X₁, X₂, X₃ ≥ 0 (only positive values are allowed)Thus, the linear programming model for maximizing total profit contribution for HartManufacturingis as follows:Maximize Z = 25X₁ + 28X₂ + 30X₃Subject to:2X₁ + 4X₂ + 3X₃ ≤ 4503X₁ + 5X₂ + 2X₃ ≤ 3501X₁ + 1X₂ + 3X₃ ≤ 50X₁, X₂, X₃ ≥ 0.Learn more onlinear programminghere:brainly.com/question/14309521#SPJ1...