A small firm which produces bicycles employs both skilled workers and apprentices. Its workforce must not exceed $30$ people and it must make at least $360$ bicycles per week to satisfy demand. On average a skilled worker can assemble $24$ bicycles and an apprentice $10$ bicycles per week. Union regulations state that the number of apprentices must be less than or equal to the number of skilled workers but at least half of the number of skilled workers.

Skilled workers are paid $$1200$ a week, and apprentices $$500$ a week. How many of each should be employed to keep the wage bill as low as possible?

Formulate this problem as a linear program in standard form, but do not solve it