Question

LM.72 A potato processing company has four plants in Southeast Idaho and sources potatoes from three different farms. You need to help them develop a sourcing plan which minimizes transportation costs. The tables below show (1) how many tons of potatoes can be supplied be each farm, (2) the monthly demand for each plant, and (3) the cost per ton of shipping from each farm to each plant.

Plant 1	Plant 2	Plant 3	Plant 4
50	70	50	30

Source	Supply
Farm 1	45
Farm 2	80
Farm 3	75

From \ To	Plant 1	Plant 2	Plant 3	Plant 4
Farm 1	8	9	9	11
Farm 2	9	10	9	7
Farm 3	7	6	8	8

When assigning farms to plants, which of the following would be the best place to start? (In the answer field below write the number that corresponds to your selection. Do not put a period after the number.)

Farm 2 to Plant 4

Farm 3 to Plant 1

Farm 1 to Plant 1

Farm 3 to Plant 2

Which farm or farms will be required to supply potatoes to Plant 2? (In the answer field below write the number that corresponds to your selection. Do not put a period after the number.)

Farm 1

Farm 2

Farm 3

Farms 1 and 2

Farms 2 and 3

Farms 1 and 3

Farms 1, 2 and 3

After satisfying all the demand, which farm will have some unassigned potatoes? (In the answer field below write the number that corresponds to your selection. Do not put a period after the number.)

Farm 1

Farm 2

Farm 3

None. There is no excess supply of potatoes.

What is the lowest cost for transporting potatoes to the four plants while meeting all the demand requirements? (Display your answer as a whole number.)

Answer 1

The best place to start would be the lowest cost option, in the table of costs, minimum cost attached is 6 from Farm 3 to Plant 2 and that would be the place to start with. So option 4

The above probelem can be solved on excel solver as below, first model the entire information as follows

The formulas used are as below

Now go to data tab and under that solver section and put constraints as below, our objective is to minimize cost

Finally click on solve and keep solver solution and the final output is as below

Thus Plant 3 is supplied by Farm 3 Only

Also there are no farms who have unassigned potatoes as there is no excess supply.

Also the lowest cost is $1,475 as displayed in Total cost cell of excel.