I need to find out the constraints and the variables so that I can input and solve in excel or management scientist. I don't know how to configure this information, can someone help me?
Tots Toys makes a plastic tricycle that is composed of three major components: a handlebar-front wheel-pedal assembly, a seat and frame unit, and rear wheels. The company has orders for 12,000 of these trikes.
As indicated in the table below, the company obviously does not have the resources available to manufacture everything needed for the completion of 12000 tricycles, so it has arranged to purchase additional components, as necessary. Develop a linear programming model to tell the company how many of each component should be manufactured and how many should be purchased in order to provide 12000 fully completed tricycles at the minimum cost.
Component Plastic Time Space Man$ Pur.$
Front/ 3 / 10/ 2 / 8/ 12
Frame/ 4 / 6/ 2 / 6/ 9
Wheel/ .5 / 2/ .1 / 1/ 3
AVAILABLE /50,000 /160,000 /30,000/
There are no variables nor constraints stated...yet....
I suspect the variables will be the three assemblies, and the only constraint implied is that the number of these cannot exceed 12000 each.
There is not enought stated to determine what the problem is.
To develop a linear programming model for this problem, we need to identify the variables and constraints.
Variables:
1. Let's define:
- x1 as the number of handlebar-front wheel-pedal assemblies to be manufactured.
- x2 as the number of seat and frame units to be manufactured.
- x3 as the number of rear wheels to be manufactured.
- y1 as the number of handlebar-front wheel-pedal assemblies to be purchased.
- y2 as the number of seat and frame units to be purchased.
- y3 as the number of rear wheels to be purchased.
Constraints:
1. Demand Constraint: The company must provide 12,000 fully completed tricycles, so the total number of tricycles assembled using manufactured components and purchased components should be equal to 12,000.
- x1 + y1 = 12,000 (handlebar-front wheel-pedal assemblies)
- x2 + y2 = 12,000 (seat and frame units)
- x3 + y3 = 12,000 (rear wheels)
2. Resource Constraints: The company has limited resources available for manufacturing and purchasing each component.
- Plastic Constraint:
- 3x1 + 4x2 + 0.5x3 + 12y1 + 9y2 + 3y3 <= 50,000 (plastic availability constraint)
- Time Constraint:
- 10x1 + 6x2 + 2x3 + 8y1 + 6y2 + 2y3 <= 160,000 (time availability constraint)
- Space Constraint:
- 2x1 + 2x2 + 0.1x3 + 1y1 + 1y2 + 1y3 <= 30,000 (space availability constraint)
- Manpower Constraint:
- 8x1 + 6x2 + x3 <= 12,000 (manpower availability constraint)
3. Non-negativity Constraint: The number of components manufactured and purchased cannot be negative.
- x1, x2, x3, y1, y2, y3 >= 0
With these constraints and variables, you can formulate the linear programming model and use Excel or Management Scientist to solve it.