Now let's solve a more classic blending problem, the wine blending problem.

M$.$L$.$ Doud Wine Distributors sells a blended red wine called CMS Select to mid$-$tier restaurants for $$24$ per gallon, and they can sell as much as they make. The blend consists of Cabernet, Merlot, and Syrah $($called $$varietals$),$ and the blend may vary slightly, but the final product must contain at least $30\%$ Cabernet, $30\%$ Merlot, and $20\%$ Syrah. M$.$L$.$ Doud Wine Distributors purchases their wine from the Sonoma Valley, where they have located Cabernet, Merlot, and Syrah varietals at the prices $($dollars per gallon$)$ and quantities $($in gallons$)$ shown in the table below.

Wine

Price $/$Gal

Availability

Cabernet

$$13$

$15000$ Gallons

Merlot

$$7$

$28000$ Gallons

Syrah

$$10$

$16000$ Gallons

Blending, bottling, and packaging adds $$5$ per gallon in costs. Based on this information, how much wine of each varietal should M$.$L$.$ Doud purchase from the Sonoma Valley to make their CMS Select blend? What is their profit? How many gallons of CMS Select do they actually make?

For decision variables: C $=$ amount of Cabernet $($in gallons$)$ to purchase for the blend; M $=$ amount of Merlot $($in gallons$)$ to purchase for the blend; S $=$ amount of Syrah $($in gallons$)$ to purchase for the blend.