6690 - Using Computers in Mathematics Instruction
Danie Brink
Essay 3 Linear Programming Example
A manufacturer of kitchen units makes two types of units, A and B. Suppose he makes x units of type A and y units of type B each month. The following constraints are applicable.
1. It takes two days to put together one unit of type A and three and one third days to put together one unit of type B. The workshop is only available for 20 days per month.
2. The paint department can only handle 8 units per month.
3. At least 2 units of type A must be produced each month.
4. The number of units of type A must be at least one third of the number of units of type B.
5. Unit type A yields a profit of $700 per unit while unit B yields a profit of $900 per unit.
Instruction: How many units must be produced to optimize the profit of the factory?
All the sketches below are made in Geometer's Sketchpad.
Step1: Taking linear constraints and graphing them.
Step 2: Finding the feasable region - the region that complies with all the constraints in 1).
Step 3: Plotting the objective function on the sketch.
Step 4: Moving the objective function across the feasable region to intersect the feasable region at the optimum location in order to optimize the process.
To see an animated version of this sketch, click here
We can clearly see that the optimum production will happen at point A. To solve for the coordinates of this point, we can solve simultaneously for g(x) and f(x). The coordinates of point A is ( 5 ; 3 ) which will yeils the maximum profit of $6200 per month.
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