An engineering company has three divisions (design, production, testing) with a combined annual budget of million. Production has an annual budget equal to the combined annual budgets of design and testing. Testing requires a budget of at least . What is the production budget and the maximum possible budget for the design division?
Let be the design budget, be the production budget, and be the be the testing budget. Then . Since the annual production budget is equal to the combined design and testing budgets, we have .
This gives
Where . Since the testing budget needs to be at least and can't be more than (since testing shares a budget of with design). Thus , and it follows that
So the production budget is and the max design budget is .