Hart Manufacturing makes three products. Each product requires manufacturing operations in three departments: A, B, and
Posted: Wed Jul 06, 2022 11:57 am
Hart Manufacturing makes three products. Each product requiresmanufacturing operations in three departments: A, B, and C. Thelabor-hour requirements, by department, are as follows.
During the next production period, the labor-hours available are450 in department A, 350 in department B, and 50 in department C.The profit contributions per unit are $25 for product 1,$27 for product 2, and $29 for product 3.
(a) Formulate a linear programming model for maximizing totalprofit contribution.(Let Pi = unitsof product i produced,for i = 1, 2, 3.)
Max: ___
s.t.
Department A: ___
Department B: ___
Department C: ___
P1, P2, P3 ≥ 0
(b) Solve the linear program formulated in part (a). How much ofeach product should be produced, and what is the projected totalprofit contribution (in dollars)?
(P1, P2, P3)= (_______) with profit $___
(c) After evaluating the solution obtained in part (b), one ofthe production supervisors noted that production setup costs hadnot been taken into account. She noted that setup costs are$380 for product 1, $580 for product 2, and $630 forproduct 3. If the solution developed in part (b) is to be used,what is the total profit contribution (in dollars) after takinginto account the setup costs?
(d) Management realized that the optimal product mix, takingsetup costs into account, might be different from the onerecommended in part (b). Formulate a mixed-integer linear programthat takes setup costs into account. Management also stated that weshould not consider making more than 140 units of product1, 185 units of product 2, or 195 units ofproduct 3.(Let Pi =units of product i producedand yi bethe 0-1 variable that is one if any quantity ofproduct i is produced and zero otherwise,for i = 1, 2, 3.)
What is the objective function of the mixed-integer linearprogram?
Max: ___
In addition to the constraints from part (a), what otherconstraints should be added to the mixed-integer linearprogram?
s.t.
units of Product 1 produced: ___
units of Product 2 produced: ___
units of Product 3 produced: ___
P1, P2, P3 ≥ 0; y1, y2, y3 =0, 1
(e) Solve the mixed-integer linear program formulated in part(d). How much of each product should be produced, and what is theprojected total profit (in dollars) contribution?
(P1, P2, P3, y1, y2, y3)= (___) with profit $___
.
During the next production period, the labor-hours available are450 in department A, 350 in department B, and 50 in department C.The profit contributions per unit are $25 for product 1,$27 for product 2, and $29 for product 3.
(a) Formulate a linear programming model for maximizing totalprofit contribution.(Let Pi = unitsof product i produced,for i = 1, 2, 3.)
Max: ___
s.t.
Department A: ___
Department B: ___
Department C: ___
P1, P2, P3 ≥ 0
(b) Solve the linear program formulated in part (a). How much ofeach product should be produced, and what is the projected totalprofit contribution (in dollars)?
(P1, P2, P3)= (_______) with profit $___
(c) After evaluating the solution obtained in part (b), one ofthe production supervisors noted that production setup costs hadnot been taken into account. She noted that setup costs are$380 for product 1, $580 for product 2, and $630 forproduct 3. If the solution developed in part (b) is to be used,what is the total profit contribution (in dollars) after takinginto account the setup costs?
(d) Management realized that the optimal product mix, takingsetup costs into account, might be different from the onerecommended in part (b). Formulate a mixed-integer linear programthat takes setup costs into account. Management also stated that weshould not consider making more than 140 units of product1, 185 units of product 2, or 195 units ofproduct 3.(Let Pi =units of product i producedand yi bethe 0-1 variable that is one if any quantity ofproduct i is produced and zero otherwise,for i = 1, 2, 3.)
What is the objective function of the mixed-integer linearprogram?
Max: ___
In addition to the constraints from part (a), what otherconstraints should be added to the mixed-integer linearprogram?
s.t.
units of Product 1 produced: ___
units of Product 2 produced: ___
units of Product 3 produced: ___
P1, P2, P3 ≥ 0; y1, y2, y3 =0, 1
(e) Solve the mixed-integer linear program formulated in part(d). How much of each product should be produced, and what is theprojected total profit (in dollars) contribution?
(P1, P2, P3, y1, y2, y3)= (___) with profit $___
.