Dutch Auction Weeks ago, the consumer products giant, Unilever,

announced plans to buy back $900,000$ shares using a Dutch auction. Since

then the company has solicited interest from shareholders by asking how

many shares they would tender at different prices. The information they

collected appears in the following table:

a$.$ What is the average price that the company will pay to buy back shares?

b$.$ Is the offer oversubscribed or undersubscribed?

c$.$ What percentage of the shares offered by stockholders that will

be repurchased?

Offer Price

Total Shares Tendered

$$$$57\mathrm{.}00$

$215$ comma $000$

$$$$57\mathrm{.}20$

$330$ comma $000$

$$$$57\mathrm{.}40$

$485$ comma $000$

$$$$57\mathrm{.}60$

$670$ comma $000$

$$$$57\mathrm{.}80$

$820$ comma $000$

$$$$58\mathrm{.}00$

$930$ comma $000$