Part I. Find the vertex of the following quadratic equations and determine whether the vertex is a maximum point or minimum point.

Exercise Procedure Vertex Maximum point or Minimum point

1. y = -3x^2 + 12x - 20

2. y = 5x^2 + 10x - 3

3. y = x^2 + 12x

4. y = -x^2 - 8

Part II. Determine the equilibrium point in the following problems. Explain, with at least 2 complete sentences, what significance does this point have in each of the situations.

1. Fixed costs for producing a certain item are $ 5,000 per month and variable costs are $ 3.50 per unit. If the producer sells each of the items at $ 6.00. Determine and

explain the equilibrium point.

2. The cost of producing x items is given by yc = 2.8x + 600, where yc is the total cost to produce x items. Each item x produced is sold at $ 4.00.

a. Find the equilibrium point.

b. If it is known that at least 450 units will be sold, what should the fixed price of each item be to ensure there are no losses?

3. The cost to produce x items per week is given by C = 1,000 + 5x. If each item can be sold at $7.00

a. Determine the equilibrium point.

b. If the manufacturer can reduce variable costs to $ 4 per item increasing fixed costs at $ 1,200 a week, would it be convenient to do so?