Question

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 = 65Q1 + 5Q1² + 96
Spartanburg: Cost = 21Q2 + 3Q2² + 147

Where
	Q1 = number of chairs produced at Aynor
	Q2= number of chairs produced at Spartanburg

Andalus needs to manufacture a total of 50 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  chairs at Aynor for a cost of $   and  chairs at Spartanburg for a cost of $  . The total cost is $  .

Answer 1

are the number of chairs produced at Aynor, Spartanburg respectively

Let be the cost of chairs produced at Aynor, Spartanburg respectively

Total of 50 chairs need to be produced

Total cost,

Put in above equation

Differentiate above equation with respect to and equate to zero to maximize C

Therefore the optimal solution is to produce 16 chairs at Aynor for a cost of $2416 and 34 chairs at Spartanburg for a cost of $4329. The total cost is $6745.