Problem 3 Figure below shows a quick-return mechanism with dimensions. a) Use a graphical method to calculate the accelerations of points A, B, and C for the position shown. W210 rad/sec CCW b) Use an analytical method to calculate the accelerations of points A, B, and C for one revolution of the input link. 210 rad/sec CCW 6 C L2 = 1.00 in L4 = 4.76 5 B A L5= 4.55 2.86 in 02 = 99° 0402 = = 1.69 @ 15.5°

Exercise2: A company makes iron benches and wants to determine the break-even point. The total fixed cost for the business is $60,000 and the variable cost is $40 per bench. It sells the bench for $100 per unit. Determine the BEP and construct a graph.

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Consider the data points in the table below: Y 120- Y 1.0 80.0 2.0 60 0 100- 3.0 40.0 4.0 20.0 5.0 0.0 80- Using the multipoint curve drawing tool, in the graph to the right, plot each point in the table above. Carefully follow the instructions above and only draw the required object. 60- 40- 20 0-

Solve for x for the following equation: 4ln(3x-8) = 60

New ads have been proposed and cost the company $5000 to run in each time slot. If the extra sales from each new ad are determined be sales = 11000 - 30ad. How many ads should be run? (enter as an integer).

Miles Mowed Labor Month and Cleaned Costs 240 $6,800 305 7,680 325 8,310 275 7,200 220 6,550 200 5,760 75 4,960 April May June July August September October Use the information from the high- and low-volume months to develop a cost-estimating equation for monthly labor costs. Monthly labor costs = $ 3955 + $ 13.4 X Plot the data on a scatter diagram. Using the information from representative high- and low volume months, use the high- low method to develop a cost-estimating equation for monthly labor costs. Monthly labor costs 3,350 + $ = $ Check Adjust the equation developed in requirement (b) to incorporate the effect of an anticipated 5% increase in wages. Monthly labor costs 325 x + $ 14.07 X X 14.07 X X $

Use graphical method to solve the following LPP: Maximise Z = x +4y Subject to the constraints: x + y < 1 2x + 2y 2 4 *2 0, y 2 0

a. Prepare the scatter diagram and insert the trendline or line of best fit. Use a scale of 2 cm to represent 1,000 units on the x-axis & 2 cm to represent $50,000 on the y-axis. b.  Using the line of best-fit, determine the company’s fixed cost per month and the variable cost per unit. (Use 0 & 5,000 units.)

What is the optimal number of clusters based on this graph? Average silhouette width 0.3 0.2 0.1 0.0- 07 02 05 O 10 Optimal number of clusters Silhouette method 12 3 6 7 4 5 Number of clusters k 8 9 10