Fresh Smoothies purchases fresh fruit and vegetables for their smoothies every week. Any produce left

over when a new shipment arrives is salvaged and usually used by other companies to produce jams,

jellies, and packaged juices. In the case that they don$$t have enough fresh fruit or vegetables to cover

the demand for the week, each store buys the necessary ingredients from local grocery stores at a price

higher than the negotiated price with the primary supplier.

Steve is in charge of the company$$s revenue management strategy and has recently completed a course

on data analytics that has caused him to question some company decisions. In particular, he wondered

why the company charges the prices they do and why they order the quantities of ingredients. Did they

know something he didn$$t know about the sensitivity of demand to changes in price and the distribution

of demand?

After significant debate with Charlie, whose approval was required for pricing changes, Steve finally got

approval to do a simple experiment at a single store with a single smoothie flavor: strawberry.

The approved plan included two weeks with a variation in price. The first week, the price would be

$$4\mathrm{.}00$; and the second week, the price would be $$6\mathrm{.}00.$ All other smoothie prices would remain constant

during the two weeks. Historically, the price of the strawberry smoothie had been $$5\mathrm{.}00$; and they had

always ordered the ingredients necessary to produce $410$ strawberry smoothies each week. To

complete the data acquisition, Steve tracked down the sales figures for the previous $30$ weeks. During

this $30-$week time frame, there hadn$$t been any store$-$wide promotional sales; and the prices of all

smoothie flavors had remained constant. The $30-$week sales figures are shown in the table below.

Week Sales Week Sales Week Sales

$14171141321352$

$23761236622398$

$34061339723404$

$43481442524405$

$54021541825468$

$64001641726379$

$74001743027408$

$83451838528443$

$93801942729359$

$104312040730432$

After waiting for what felt like an eternity, at last the experiment was complete and the data compiled.

The observed demand for the strawberry smoothie during the two experimental weeks is included in

the table below.

Price Observed

Demand

$$4\mathrm{.}00494$

$$6\mathrm{.}00344$