Consider the problem: Determine whether the following system of 4x 8x ations is consistent: 2y + 7z = -5 3y + 10z = -3

For the following system to be consistent, 4x+5y-3z = 3 -22x+1y+kz -9x+3y-8z =-14 = -4 we must have, k #

Andalus Furniture Company has two manufacturing plants, one at Aynor and another at Spartanburg. The cost of producing Q₁ kitchen chairs at Aynor is 2 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 130 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 Chairs at Spartanburg Total Production cost Q2 = = C = $

Need only a handwritten solution only (not a typed one).