Bear construction is supplying building materials for a new mall construction project in Montana. Their contract calls for a total of 150,000 tons of material to be delivered over a three-week period. Bear's supply depot has access to three modes of transportation: a trucking fleet, railway delivery, and air cargo transport. Their contract calls for 140,000 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 35% of the total delivered to be delivered by trucking, at least 45% of the total delivered to be delivered by railway, and up to 10% 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	50	55	10
3	55	45	5
Costs ($ per 1000 tons)	$200	$140	$500

The following is the LP model for this problem. The decision variables are shown in cells B3: D5. Cells E3:E5 and B6:B8 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 = 50)

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 0.10*250 Air mix requirement

Xij 0 for all i and j

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

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, select the best answer.

What is the objective function cell?

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

What cell constitutes the RHS of the "total required at end of three weeks" constraint?

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

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