The cost of making two products is $3 each. The first product requires 2kg and the second 4kg of material. You have at least a total of 16kg available. The time to produce the first product is 4 hrs and the second 3 hours. In total there are 24 hours available. You have an order for 2 items of the first product so must make sure you produce at least this amount.
Formulate as a linear programming problem.
Draw a graph for the problem and clearly identify the feasible solution space. Then calculate, by hand, showing all workings, the following:
(i) Optimum solution in full
(ii) Ranges for the Objective Co-efficients
(iii) Shadow Prices
(iv) Right Hand Side Ranges
Note
I have established the Min objective funtion:
Min Z = 3Y1 + 3Y2
Subject to:
2Y1 + 4Y2 => 16 (CONSTRAINT 1)
4Y1 + 3Y2 <= 24 (CONSTRAINT 2)
Y1 => 2 (CONSTRAINT 3)
Y2 => 0
And have graphed to find the solution as (printed below) be having issues with parts (ii), (ii) and (iv) of the questions:
