Suppose the order is for

of Platter A and

of Platter B. Then we have:

We want to minimize

subject to the above constraints. Let us then rewrite the above inequalities in terms of

and one of

and

, say

.

The 1st and 2nd inequalities give

, the 1st and 3rd inequalities give

, and the 2nd and 3rd inequalities give

. The minimum appears to be 855 – however

would imply

, which does not satisfy the 2nd inequality. So we must instead have

. Thus the minimum cost is $870 dollars for 10 of Platter A and 60 of Platter B.