alright.. this is the linear programming question i got..
JJ Manufacturing has three factories (1,2,3) and three distribution centers (A,B,C). shipping costs from the factories to the distrubution centers is as follows
from factory 1 to center A: $6
from factory 2 to center A: $8
from factory 3 to center A: $11
from factory 1 to center B: $5
from factory 2 to center B: $10
from factory 3 to center B: $14
from factory 1 to center c: $3
from factory 2 to center A: $8
from factory 3 to center A: $18
production capability of fact 1 = 6000
production capability of fact 2 = 8000
production capability of fact 3 = 10000
demand at distributtion center A = 7000
demand at distributtion center B = 12000
demand at distributtion center C = 5000
the product is is produced and deliverd in a lot size of 100
im at a total blank at how to write the objective function and contraints. can u please help me with this ASAP! :)
Sure! Let's break down the problem step by step.
Objective Function:
The objective function in linear programming is the function that we want to either maximize or minimize. In this case, we want to minimize the shipping costs. So, the objective function can be expressed as:
Minimize Z = 6x11 + 5x10 + 3x18 + 8x8 + 8x11 + 10x14
where x1, x2, and x3 represent the lot sizes produced at factories 1, 2, and 3, respectively.
Constraints:
Next, let's write down the constraints based on the given information.
1. Production capability constraints:
The total production from each factory should not exceed its production capability. Therefore, we have the following constraints:
x1 ≤ 6000 (Production capability of factory 1)
x2 ≤ 8000 (Production capability of factory 2)
x3 ≤ 10000 (Production capability of factory 3)
2. Demand constraints:
The total demand at each distribution center should be met. Therefore, we have the following constraints:
x1 + x2 + x3 = 7000 (Demand at distribution center A)
x1 + x2 + x3 = 12000 (Demand at distribution center B)
x1 + x2 + x3 = 5000 (Demand at distribution center C)
3. Non-negativity constraints:
The lot sizes produced cannot be negative. Therefore, we have the following constraints:
x1 ≥ 0
x2 ≥ 0
x3 ≥ 0
These constraints ensure that the lot sizes produced and delivered are non-negative and within the production capabilities and demand requirements.
Now, you have the objective function and constraints for your linear programming problem. You can use a software tool like Excel Solver or any linear programming solver to find the optimal solution that minimizes the shipping costs while satisfying all the constraints.