A biologist is developing two new strains of bacteria. Each sample of Type 1 bacteria produces four new viable bacteria, and eac
h sample of Type II bacteria produces three new viable bacteria. Altogether, at least 240 new viable bacteria must be produced. At least 20, but not more than 60, of the original samples must by Type I. Not more than 70 of the original samples can be Type II. A sample of Type I costs $5 and a sample of Type II costs $7. How many samples of each bacteria should the biologist use to minimize the cost? What is the minimum cost?