Andalus Furniture Company has two manufacturing plants, one at Aynor and another at Spartanburg. The cost of producing Q₁ kitchen chairs at Aynor is

75Q₁ + 5Q₁² + 100

and the cost of producing Q₂ kitchen chairs at Spartanburg is

25Q₂ + 2.5Q₂² + 140.

Andalus needs to manufacture a total of 100 kitchen chairs to meet an order just received. How many chairs should be made at Aynor and how many should be made at Spartanburg in order to minimize total production cost? What is the total production cost (in dollars)?

Chairs at Aynor Q_{1 =}

Chairs at Spartanburg Q₂₌

Total Production cost C=