Alternative Example $($Minimization$)$:$$A fabric firm has received an order for cloth specified to contain at least $45$ pounds of cotton and $25$ pounds of silk. The cloth can be woven out on any suitable mix of two yarns, A and B$.$ Material A costs $$3$ per pound, and B costs $$2$ per pound. They contain the following percentages of cotton and silk $($by weight$)$:A$=30\%$cotton and $60\%$silk $,$ B$=50\%$cotton and $10\%$silk