Question

You have been asked to plan for the cost-optimal fulfillment of demand at four cities in Africa-Johannesberg, Lusaka, Mombasa, and Nairobi. The relevant costs and demand (in kilograms) are shown in the table to your left. 1. In the box to your right of the constraint Please explain the function of each of the following constraints in the Solver model (10 POINTS EACH) Constraint $C22:$F22=0 $C26:$C29>=0 $G17:$G20=BINARY $G6:$G9>=$H17:$H20 If you fulfill the given demands under these constraints what is the lowest cost you will incur? (10 POINTS)

Transportation Cost per kg
	To
From	Johannesberg	Lusaka	Mombasa	Nairobi	Capacity	Fixed Cost
Johannesberg	1	4.5	8.5	9.5	40000	90000
Lusaka	3.5	1	6.5	6.85	10000	65000
Mombasa	8.25	7.85	1	2	15000	80000
Nairobi	8.75	7.15	2.25	1	25000	75000
Demand	30000	15000	20000	25000
Decision Variables
Flows	To				Location
From	Johannesberg	Lusaka	Mombasa	Nairobi	Open/close	Total
Johannesberg	0	0	0	0	0	0
Lusaka	0	0	0	0	0	0
Mombasa	0	0	0	0	0	0
Nairobi	0	0	0	0	0	0
Total	0	0	0	0	0	0
Unmet Demand	30000	15000	20000	25000
Unused Capacity
Johannesberg	0
Lusaka	0
Mombasa	0
Nairobi	0
TOTAL COST
Fixed	0
Variable	0
Total	0

Answer 1

As the capacity and demand are same, there will not be any unused capacity.

Now explaining the constraints, ( should have used name ranges, it would have been easier)

C22:F22 = 0 : It means, after solver completes the function, the unmet demand(C22:F22) should be zero.

Otherwise, as we keep the cost to minimum, solver will not allocate at all.

C26:C29 >= 0 : It means, unused capacity should be zero or more, as solver might allocate more than capacity, same as above.

G6:G9 >= H17:H20 : Same as above, allocation cannot exceed capacity.

G17:G20 are binary : As there are only two cases, whether open or close, we need only 0 / 1 (Binary) in those cells.

Answer $455,000

Good luck