Problem description (read quickly and do not implement in Excel):

The facilities manager at your company is planning to apply fertilizer to the grass area surrounding the office building. The grass needs at least the following amounts of minerals:

Mineral	Nitrogen	Phosphorus	Potash
Minimum amount required (lbs)	12	14	18

Three kinds of commercial fertilizers are available with mineral contents per 1,000 lbs and prices per 1,000 lbs given in the following table:

Fertilizer	Nitrogen (lbs)	Phosphorus (lbs)	Potash (lbs)	Price ($)
A	20	10	5	10
B	10	5	15	8
C	15	10	5	7

To help the manager to decide how much of each fertilizer to purchase to satisfy the requirements at the minimum cost, you have setup an optimization model with decisions (in 1,000 lbs): A, B, C - amounts of fertilizer of each kind to purchase.

Min_A,B,C 10A + 8B + 7C

s.t.

20A + 10B + 15C 12

10A + 5B + 10C 14

5A + 15B + 5C 18

A, B, C are non-negative

Now, the analysis (use this info to answer questions).

Solver generated the following sensitivity report for your model.

What is the optimal purchase plan? Please mark your answer in the list below.

A. Deliver 23.20 lbs of nitrogen, 14 lbs of phosphorus, and 18 lbs of potash to the grass area.

B. Allowable Increase of B is 13 and Allowable Increase of C is 3.

C. Purchase $3,000 of fertilizer A.

D. Purchase 880 lbs of fertilizer B and 960 lbs of fertilizer C.

E. Purchase fertilizers such that the total cost is $13,760

F. Allowable Increase of Nitrogen is 11.2 and Allowable Increase of Phosphorus is 22 and Allowable increase of Potash is 24.

G. Purchase fertilizers such that the grass area receives at least 12 lbs of nitrogen, 14 lbs of phosphorus and 18 lbs of potash.

H. Do not use fertilizer A.

Target Cell (Min) Cell Name $E$8 Cost Final Value 13.76 Adjustable Cells Name Cell $B$5 A $C$5 B $D$5 Final Value 0.000 0.880 0.960 Reduced Cost 3.000 0.000 0.000 Objective Allowable Allowable Coefficient Increase Decrease 10 1E+30 3 8 13 4.5 7 3 4.333333333 Constraints Cell Name $E$11 Nitrogen $E$12 Phosphorus $E$13 Potash Final Value 23.20 14.00 18.00 Shadow Price 0.00 0.52 0.36 Constraint Allowable R.H. Side Increase 12 11.2 14 22 18 24 Allowable Decrease 1E+30 8 11