Question $2$

Guelph 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$)$:

$\backslash$table$[[$Yarn$,$Cotton $(\%),$Silk $(\%)],[$A$,30,50],[B,60,10]]$

What quantities $($pounds$)$ of A and $B$ yarns should be used to minimize the cost of this order?

a$.$ State the objective function

b$.$ State the constraints

c$.$ Use the corner point graphical approach

d$.$ Use the isocost approach