The president of ChemTech is trying to decidewhether to start a new product line or purchase asmall company. It is not financially possible to doboth. To make the product for a 3-year periodwill require an initial investment of $250,000.The expected annual cash flows with probabilitiesin parentheses are $75,000 (0.5), $90,000(0.4), and $150,000 (0.1). To purchase the smallcompany will cost $450,000 now. Market surveysindicate a 55% chance of increased sales for thecompany and a 45% chance of severe decreaseswith an annual cash flow of $25,000. If decreasesare experienced in the first year, the companywill be sold immediately (during year 1) at aprice of $200,000. Increased sales could be$100,000 the first 2 years. If this occurs, a decisionto expand after 2 years at an additionalinvestment of $100,000 will be considered. Thisexpansion could generate cash flows with indicatedprobabilities as follows: $120,000 (0.3),$140,000 (0.3), and $175,000 (0.4). If expansionis not chosen, the current size will be maintainedwith anticipated sales to continue. Assume thereare no salvage values on any investments. Use thedescription given and a 15% per year return to dothe following: (a) Construct a decision tree including all valuesand probabilities. (b) Determine the expected PW values at theexpansion/no expansion decision nodeafter 2 years provided sales are up. (c) Determine what decision should be madenow to offer the greatest return possible forChemTech. (d ) Explain in words what would happen to theexpected values at each decision node if theplanning horizon were extended beyond3 years and all cash flow values continued asforecasted in the description.

LECTURE 10 Moment about an axis Moment of a scalar force about any point is to the shortest perpendicular distance To find the moment around an axis (a) We take the dot product of the unit vector of a with (r x F), the cross product of r and F For example, you should set up a problem like so… uax uay uaz rx ry rz Fx Fy Fz ua is the unit vector along the a axis r is the position vector from the a axis to where the force is applied F is the force applied Note: (P x Q) ∙ R = R ∙ (P x Q) LECTURE 11 MOMENT OF A COUPLE A couple is 2 parallel forces with the same magnitude pointing in opposite directions Moment by a couple is defined as Mo = Fd F is the magnitude of the force and d is the perpendicular distance between the