1. quantitative analysis involves the use of mathematical equations or relationships in analyzing a particular problem. in most cases, the results of quantitative analysis will be one or more numbers that can be used by managers and decision makers in making better decisions. (1) defining the problem, (2) developing a model, (3) acquiring input data, (4) developing a solution, (5) testing the solution, (6) analyzing the results, and (7) implementing the results. which step is the most difficult? 2. true of false the phrase ‘garbage in, garbage out’ highlights the importance of acquiring accurate input data. if the input data is inaccurate then no matter how good the model, the results produced will be misleading. 3. the break-even point is the number of units that must be sold to make zero profits. to compute this, we must know: a) the selling price, the fixed cost, and the variable cost per unit. b) the selling price, the variable cost per unit, the profit. c). the fixed cost, the variable cost per unit and the number of units. d) the variable cost per unit, the number of units and the profit. 4. which of the following categories of business analytics involves the use of optimization models? a) descriptive b) predictive c) prescriptive d) none of the above 5. true of false a union is the set of all outcomes that are contained in either of two or more events.