Duck construction is supplying building materials for a new mall construction project in Oregon. Their contract calls for a total of 250,000 tons of material to be delivered over a three-week period. Duck's supply depot has access to three modes of transportation: a trucking fleet, railway delivery, and air cargo transport. Their contract calls for 120,000 tons delivered by the end of week one, 80% of the total delivered by the end of week two, and the entire amount delivered by the end of week three. Contracts in place with the transportation companies call for at least 45% of the total delivered to be delivered by trucking, at least 40% of the total delivered to be delivered by railway, and up to 15% of the total delivered to be delivered by air cargo. Unfortunately, competing demands limit the availability of each mode of transportation each of the three weeks to the following levels (all in thousands of tons):

Week	Trucking Limits	Railway Limits	Air Cargo Limits
1	45	60	15
2	60	55	10
3	55	45	5
Costs ($ per 1000 cans)	$200	$140	$500

The following is the LP model for this problem. The decision variables are shown in cells N52:P54. Cells Q52:Q54 and N55:P55 are functions of the decision variables.

Let Xij = amount shipped by mode i in week j (thousands of tons)

where i = 1(Truck), 2(Rail), 3(Air)

and j = 1, 2, 3

WLij = weekly limit of mode i in week j (as provided in above table, for example WL12 = 60)

MIN: 200(X11 + X12 + X13) + 140(X21 + X22 + X23) + 500(X31 + X32 + X33)

Subject to: Xij WLij for all i and j Weekly limits by mode

X11 + X12 + X13 + X21 + X22 + X23 + X31 + X32 + X33 250 Total required at end of three weeks

X11 + X21 + X31 + X12 + X22 + X32 200 Total required at end of two weeks

X11 + X21 + X31 120 Total required at end of first week

X11 + X12 + X13 0.45*250 Truck mix requirement

X21 + X22 + X23 0.40*250 Rail mix requirement

X31 + X32 + X33 0.15*250 Air mix requirement

Xij 0 for all i and j

The following is a snapshot of the excel worksheet setup for the problem:

Costs	200	140	500
	by Truck	by Rail	by Air	Totals	Required
Week 1	45	60	15	120	120
Week 2	60	45	0	225	200
Week 3	13	12	0	250	250
Shipped by	118	117	15
Percentage	0.45	0.4	0.15
Total Limit	112.5	100	37.5
				Total Cost	$47,480
		Weekly	Limits
	Truck	Rail	Air
Week 1	45	60	15
Week 2	60	55	10
Week 3	55	45	5

It should be noted that the above solution is not necessarily feasible, as the problem has not necessarily been solved yet.

For each of the following questions, enter the alphanumeric name for the cell or the range as requested. For example, the cell in column A and row 10 would be entered as A10, and the range from it to cell A14 would be entered as A10:A14 . Use upper case letters to specify cells. DO NOT ENTER THE CELL VALUES (THE NUMERIC VALUES) FOR ANY OF THE FOLLOWING ANSWERS; ENTER THE ALPHANUMERIC CELL NAME USING THE SPECIFIED FORMAT.

What is the objective function cell?

What cell range constitutes the RHS of the "weekly limits by mode" constraints?

What cell constitutes the LHS of the "total required at end of two weeks" constraint?

What cell constitutes the LHS of the "truck mix requirement" constraint?

What cell constitutes the RHS of the "air mix requirement" constraint?