Problem $12-27($Algorithmic$)$

Andalus Furniture Company has two manufacturing plants, one at Aynor and another at Spartanburg. The cost in dollars of producing a kitchen chair at each of the two plants is given here.

Aynor: Cost $=74$Q$1+6$Q$12+108$

Spartanburg: Cost $=20$Q$2+3$Q$22+144$

Where

Q$1=$ number of chairs produced at Aynor

Q$2=$ number of chairs produced at Spartanburg

Andalus needs to manufacture a total of $30$ 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? When required, round your answers to the nearest dollar.

The optimal solution is to produce fill in the blank $1$

chairs at Aynor for a cost of $ fill in the blank $2$

and fill in the blank $3$

chairs at Spartanburg for a cost of $ fill in the blank $4$

$.$ The total cost is $ fill in the blank $5$

$.$