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.
Department
Product
1
Product
2
Product
3
A
1.50
3.00
2.00
B
2.00
1.00
2.50
C
0.25
0.25
0.25
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 $27 for product 1,
$29 for product 2, and $31 for product 3.
(a)
Formulate a linear programming model for maximizing total profit
contribution.
(Let Pi = units
of product i produced,
for i = 1, 2, 3.)
Max (need answer here)
s.t.
Department A (need answer here)
Department B (need answer here)
Department C (need answer here)
P1, P2, P3 ≥ 0
(b)
Solve the linear program formulated in part (a). How much of
each product should be produced, and what is the projected total
profit contribution (in dollars)?
(P1, P2, P3)
= (need answer/equation/inequality here) with profit $ (need
answer here)
(c)
After evaluating the solution obtained in part (b), one of the
production supervisors noted that production setup costs had not
been taken into account. She noted that setup costs are
$420 for product 1, $520 for product 2, and $570 for
product 3. If the solution developed in part (b) is to be used,
what is the total profit contribution (in dollars) after taking
into account the setup costs?
$ (need answer here)
(d)
Management realized that the optimal product mix, taking setup
costs into account, might be different from the one recommended in
part (b). Formulate a mixed-integer linear program that takes setup
costs into account. Management also stated that we should not
consider making more than 170 units of product
1, 175 units of product 2, or 185 units of
product 3. (Let
Pi = units
of product i produced
and yi be
the 0-1 variable that is one if any quantity of
product i is produced and zero otherwise,
for i = 1, 2, 3.)
What is the objective function of the mixed-integer linear
program?
Max (need answer here?)
In addition to the constraints from part (a), what other
constraints should be added to the mixed-integer linear
program?
s.t.
units of Product 1 produced (need answer here?)
units of Product 2 produced(need answer here)
units of Product 3 produced(need answer here)
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 the
projected total profit (in dollars) contribution?
(P1, P2, P3, y1, y2, y3)
= (need answer here) with profit $ (need answer here)
.