How to solve

Dutch Auction Weeks ago, the consumer products giant, Unilever, announced plans to buy back $700,000$ 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?

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

$($Round to the nearest cent.$)$

Data table

$($Click on the following icon in order to copy its contents into a spreadsheet.

$\backslash$table$[[$Offer Price,Total Shares Tendered$],[$$$54\mathrm{.}00,210,000],[$$$54\mathrm{.}10,340,000],[$$$54\mathrm{.}20,490,000],[$$$54\mathrm{.}30,655,000],[$$$54\mathrm{.}40,800,000],[$$$54\mathrm{.}50,940,000]]$