Question

Very Good Juice Company produces five different juices: cherry, apple, orange, pineapple, and lemon. Each month, management is faced with the decision of how much of each product to produce for the next month. Virtually no finished product inventory is carried, but ample supplies of the raw materials are on hand. The products yield different profits and require different amounts of machine time in each of three processes (blending, straining, and bottling). The relevant data, per 1,000 gal as well as the minutes available per process appear in the table below.

	Apple	Cherry	Lemon	Orange	Pineapple	Minutes Available
Blend	23	22	18	19	19	5000
Strain	22	40	20	34	22	3000
Bottle	10	10	10	10	10	5000

	Apple	Cherry	Lemon	Orange	Pineapple
Profit $/1000gal.	$800	$320	$1120	$1440	$800
Max Sales 0gal.	20	30	50	50	20
MMin Sales 0gal.	10	15	20	40	10

Sensitivity Report

Adjustable Cells Cell Name $B$16 Production Apple $C$16 Production Cherry SD$16 Production Lernon SE$16 Production Orange $F$16 Production Pineapple Final Reduced Objective Allowable Allowable Value Cost Coefficient Increase Decrease 100 8004321E+30 15 0 320 1920 1E+30 1120 1E+30 2729411765 40 1440 1E+30 0 800 432 1 E+30 30 464 10 15 30 50 10 0 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price RH Side Increase Decrease $B$17 Production (aux var) Apple 10 0 20 1E+30 10 $C$17 Production (aux var) Cherry 15 30 1E+30 SD$17 Production (aux var) Lemon 0 50 1E+30 20 $E$17 Production (aux var) Orange 40 0 1E+30 $F$17 Production (aux var) Pineapple 10 20 1E+30 10 $B$17 Production (aux var) Apple 10 432 10 9.090909091 10 $C$17 Production (aux var) Cherry 15 -1920 15 10 $D$17 Production (aux var) Lemon 30 0 20 1E+30 SE$17 Production (aux var) Orange 40 464 40 5.882352941 11.76470588 $F$17 Production (aux var) Pineapple 10 432 10 9.090909091 10 $B$20 Blend Minutes Used 2050 5000 1E+30 2950 $B$21 Strain Minutes Used 3000 56 3000 400 200 SBS22 Bottle Minutes Used 1050 0 5000 1E+30 3950 5 10

Which of the upper bound constraints are binding?

A. Only Lemon

B. All of them

C. None of them

D. Only Apple, Cherry, Orange, and Pineapple

Answer 1

The right answer is

C. None of them

The reason is that the quantity produced of each type of juice is less than the maximum sales goal. Strain minutes used are getting exhausted before the upper bound constraint on any of the juice's quantity is reached.