8.3 CHAPTER 8. LINEAR PROGRAMMING
Step 1 : Identify the decision variables
Let the number of kettles be x and the number of toasters be y and write down
two constraints apart from x≥ 0 and y≥ 0 that must be adhered to.
Step 2 : Write constraint equations
Since there will be at least 10 of each prize we can write:
x≥ 10
and
y≥ 10
Also, the store promisedto give away at least 40 prizes in total. Therefore:
x +y≥ 40
Step 3 : Write the objective function
The cost of manufacturing a kettle is R 60 and a toaster is R 50. Therefore the cost
the total cost C is:
C = 60x + 50y
Step 4 : Sketch the graph of thefeasible region
10
20
30
40
50
60
70
80
90
100
10 20 30 40 50 60 70 80 90 10 0
x
y
A
B
Step 5 : Determine vertices of feasible region
From the graph, the coordinates of vertex A are (30; 10) and the coordinates of
vertex B are (10; 30).
Step 6 : Draw in the search line
The search line is the gradient of the objective function. That is, if the equation
C = 60x + 50y is now written in the standard form y = ..., then the gradient is:
m =−
6
5
,
which is shown with thebroken line on the graph.
