Kroger, the country's leading grocery$-$only chain, added a line of private label organic and natural foods call

Simple Truth to its stores. If you've priced organic foods, you know they are more expensive. For example, a

dozen conventionally farmed Grade$-$A eggs at Kroger costs consumers $$1\mathrm{.}50,$ whereas Simple Truth eggs are

priced at $$2\mathrm{.}70$ per dozen. One study found that, overall, the average price of organic foods is $85$ percent more

than conventional foods. However, if prices get too high, consumers will not purchase the organic options. One

element of sustainability is organic farming, which costs much more than conventional farming, and those

higher costs are passed on to consumers. Suppose that a conventional egg farmer's average fixed costs per

year for conventionally farmed eggs are $$1$ million per year, but an organic egg farmer's fixed costs are three

times that amount. The organic farmer's variable costs of $$1\mathrm{.}60$ per dozen are twice as much as a

conventional farmer's variable costs. Most large egg farmers sell eggs directly to retailers. If Kroger's margin is

$30$ percent based on its retail price, the farmer's price per dozen to the retailer for conventional eggs is $$1\mathrm{.}05$

and for organic eggs is $$1\mathrm{.}89.$ How many dozen eggs does a conventional farmer need to sell to break even?

How many does an organic farmer need to sell to break even?

The variable cost per dozen of conventional eggs is $

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