Thread: linear programming/solver

i am completely stuck on this problem, i cannot figure out all of the contraints or what Z is. can i have to equations for Z? i know how to do in solver but i just cant figure out out to fomulate the problem

Frandec Company manufactures, assembles, and rebuilds material handling equipment used in warehouses and distribution centers. One product, called a Liftmaster, is assembled from four components: a frame, a motor, two supports, and a metal strap. Frandec’s production schedule calls for 5000 Liftmasters to be made next month. Frandec purchases the motors from an outside supplier, but the frames, supports and straps may either be manufactured by the company or purchased from an outside supplier. Manufacturing and purchase costs per unit are shown.
Component
Manufacturing Cost
Purchase Cost
Frame
$38.00
$51.00
Support
11.50
15.00
Strap
6.50
7.50

Three departments are involved in the production of these components. The time (in minutes per unit) required to process each component in each department and the available capacity (in hours) for the three departments are as follows.
capacity (in hours) for the three departments are as follows.
DEPARTMENT
Component
Cutting
Milling
Shaping
Frame
3.5
2.2
3.1
Support
1.3
1.7
2.6
Strap
1.8
---
1.7
Capacity (hours)
350
420
680

Originally Posted by thrasher

i am completely stuck on this problem, i cannot figure out all of the contraints or what Z is. can i have to equations for Z? i know how to do in solver but i just cant figure out out to fomulate the problem

Frandec Company manufactures, assembles, and rebuilds material handling equipment used in warehouses and distribution centers. One product, called a Liftmaster, is assembled from four components: a frame, a motor, two supports, and a metal strap. Frandec’s production schedule calls for 5000 Liftmasters to be made next month. Frandec purchases the motors from an outside supplier, but the frames, supports and straps may either be manufactured by the company or purchased from an outside supplier. Manufacturing and purchase costs per unit are shown.

Component
Manufacturing Cost
Purchase Cost
Frame
$38.00
$51.00
Support
11.50
15.00
Strap
6.50
7.50

Three departments are involved in the production of these components. The time (in minutes per unit) required to process each component in each department and the available capacity (in hours) for the three departments are as follows.
capacity (in hours) for the three departments are as follows.
DEPARTMENT
Component
Cutting
Milling
Shaping
Frame
3.5
2.2
3.1
Support
1.3
1.7
2.6
Strap
1.8
---
1.7
Capacity (hours)
350
420
680

Let the variables be $\displaystyle R$, $\displaystyle U$ and $\displaystyle T$ the number of frames, supports and straps manufactured. The objective to be mininmise is the total cost:

$\displaystyle f(R,U,T)=38R+51(5000-R)+11.5U+15(5000-U)+6.5T+7.5(5000-T)$

or:

$\displaystyle f(R,U,T)=367500-13R-3.5U-T$

which if you prefer is minimised by maximising:

$\displaystyle g(R,U,T)=13R+3.5U+T$.

Then we have the capacity constraints:

$\displaystyle 3.5R+1.3U+1.8T \le 350$

$\displaystyle 2.2R+1.7U \le 420$

$\displaystyle 3.1R+2.6U+1.7T \le 680$

Then the usual positivity constraints and also:

$\displaystyle R \le 5000$

$\displaystyle U \le 5000$

$\displaystyle T \le 5000$.

CB