Orange products has two plants "I" and "II" which produce smart watch hardware. There are 100 units of hardware available in plant "I" and 110 units available in plant "II". The hardware are to be shipped to two main assembly plants A and B.

The shipping costs per unit to assembly plants A and B from Plants I and II are as follows:

To

From A B

I 100 60

II 120 70

a) In November, Assembly A needs 80 units and assembly B needs 70 units of hardware. Find how many units must be shipped from either plant I and II to each one of A and B so that the shipping costs are to be kept to the minimum.

b) How much can the shipment cost from plant "I" to plant "A" change without affecting the optimal solution? (Find the range of the cost per unit without affecting the solution)

c) Find the range for number of units (instead of 110 units) that plant "II" can provide without changing (the fact that there is an) optimal solution. Does it mean that any number in this range would not change the optimal solution? What is your interpretation of this range of numbers?

d) Find and interpret the shadow price for plant "II".

PLEASE MENTION ALL THE CONSTRAINTS