Problem $13-10$ Algo $($Generating Alternatives in Binary Optimization$)$ Detroit, Toledo, Denver, or Kansas City. The estimated annual fixed cost and the annual capacity for the four proposed plants are as follows:

$\backslash$table$[[$Proposed Plant,Annual Fixed Cost,Annual Capacity$],[$Detroit$,$$$175,000,10,000],[$Toledo$,$$$300,000,20,000],[$Denver$,$$$375,000,30,000],[$Kansas City,$$500,000,40,000]]$

The company's long$-$range planning group developed forecasts of the anticipated annual demand at the distribution centers as follows:

$\backslash$table$[[$Distribution Center,Annual Demand$],[$Boston$,20,000],[$Atlanta$,30,000],[$Houston$,20,000]]$

The shipping cost per unit from each plant to each distribution center is as follows:

$\backslash$table$[[,$Distribution Centers$],[$Plant Site,Boston,Atlanta,Houston$],[$Detroit$,5,2,3],[$Toledo$,4,3,4],[$Denver$,9,7,5],[$Kansas City,$10,4,2],[$St$.$ Louis,$8,4,3]]$

$3$

What is the optimal set of plants to open?

$q,$

$($b$)$ Using equation $13\mathrm{.}1,$ find a second$-$best solution. What is the optimal set of plants to open?

Detroit & Denver

What is the increase in cost versus the best solution from part $($a$)?$

$$290000$