# Algebraic Bases of Everyday Decisions Report

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Updated: Mar 2nd, 2022

On thinking about it, one realizes that we quite unconsciously use algebraic equations when making buying decisions from day to day. This is illustrated by the matter of determining value when scrutinizing prices at rival supermarkets.

From where we live, we can readily drive to Wal-Mart, Walgreens, CVS and Eckerd easily. Since the latter are drug chains but Wal-Mart also stocks cold remedies, I wondered whether we were right to confine our cold remedy buying to the drug chains on the assumption that retail specialization would give better value to shoppers.

Take Benadryl Allergy which comes in 100-capsule packs. The last time I checked, these retailed for \$6.94 in Wal-Mart, \$7.99 in Walgreens, \$8.29 in CVS and \$8.59 in Eckerd. Alright, so Wal-Mart has the cheapest price. That is only moderately surprising. But then I pose the question: if my sister went out to re-stock on her cosmetics and hygiene products, which she routinely does at Eckerd, is the price advantage at Wal-Mart enough to justify making the detour on the assumption that it applies to other health remedies our family buys regularly?

I of course intuitively compute for the percentage difference between Wal-Mart and every other competitor using “Percent Savings = [(Rival X – Wal-Mart)/Rival Price] X 100.” Or, more symbolically, [(B-=A)/B] X 100. Now I learn that the biggest retailer in the country sells our favorite cold and allergy remedy 13%, 16% and 19% cheaper, respectively, than at Walgreens, CVS or Eckerd. So if I save as much as 20% on every one of five drugs we regularly buy and

“total savings = \$2.00 X five” = Discount = 0.20 (Quantity)

is it worth the extra fuel cost to have to drive to Wal-Mart to take advantage of the savings?

Now I solve for fuel cost as = miles travelled X (current retail price of gasoline/mileage of family car). Substituting the three-mile distance between Wal-Mart and the highest-priced competitor, gasoline at \$1.50 to the gallon and our car’s published mileage of 15 miles to the gallon in city driving less a 15% factor for the age of the Chevy:

Distance travelled X cost per mile

D X (1.50/[original mileage – 15%])

=3 X (1.50/[15-15%]) = 3 X (1.50/12.75) = 3 X \$0.12 = \$ 0.36.

This tells me that the value of making the extra trip to Wal-Mart = cost : benefit ratio = \$0.36 to savings of \$10.00. Clearly, it is worth it to patronize Wal-Mart for the given drugs. However, my sister disagrees because, being a working mother of three, she just does not have the time to make extra shopping trips. So in her case, the saving of \$ 9.64 (\$10 less \$0.36) does not make up for the convenience of fitting more into her busy weekends by making all our health and beauty product shopping at Eckerd instead. Another practical lesson of this testing for value to shoppers is that, if I were to offer to do the shopping from a grocery list of hers and I noticed Benadryl as the day’s “hot buy” at \$2.00 less and I happened to clip a coupon the day before for an additional \$1 saving, I conclude I do not have to go to Wal-Mart any more.

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