A high quality wine is typically identified by three attributes: a$.$ Vintage, b$.$ Variety and c$.$ Region. FOr example, the optima Winery of Santa ROsa, California produced a wine with label that stated: $1984,$ cabernet Sauvignon, Sonoma COunty. The wine in the bottle may be a blend of wines, not all of which need be of vintage, variety and region specified on the label. In this case, the state of california and the U$.$S Department of Alcohol, Tobacco, and Firearms strictly enforce the following limits$.$ To receive the label $"1984,$ Cabernet Sauvignon Sonoma County," atleast $95\%$ of the contents must be of $1984$ vintage, at least $75\%$ of the contents must be cabernet Sauvignon and at least $85\%$ must be from Sonoma County.

How small might be the fraction of the wine in the bottle that is $1984$ vintage and of the cabernet Sauvignon variety and from grapes grown in Sonoma County?

What is the composition of the wine in terms of the $7$ possible ingredients combinations? $($Obviously$,$ there is an $8$th possible ingredient combination $-$ non$-84,$ non$-$Cab, and non$-$Sonoma but including such an ingredient would preclude the minimum inclusion of the ingredient with all three characteristics$)$ Use excel solver to solve.