$5-13$ Marc Simard's construction firm currently has three projects under way in various towns in Quebec. Each requires a specific supply of gravel. Three gravel pits are available in Quebec to provide for Simard's needs, but shupping costs differ from location to location. The following table summarizes the problem Simard faces.

R

TO

PROM

JOB $1$: $1083-3003$

TONNAGE ALLOWANCE

Kamouraska pit

Chicoutimi pit

SH

$$7$

$6$

$1500$

$1750$

Maniwaki pit loh requirements $($tonnes$)$

$2000$

$3$

$12$

$3000$

$1000$

$2750$

$6000$

$($a$)$ Determine Simard's optinal shipping quantities so as to minimize total transportation costs.

$($b$)$ Examining the map, Simard recognizes that lubs $1$ and $2$ are very near Maniwaki. Rather than shipping gravel directly from the Kamouraska and Chicoutimi pits to these job sites, Simard wonders if it would be better for him to consolidate shipping at Maniwaki. Given the excellent roads between major cities in Quehec, he believes he can ship gravel between Chicoutimi and Maniwaki and between Kamouraska and Maniwaki for as little as $52$ per tonne. Set up and salve Sintard's problem now with this new information.