# Determine the break-even point, where selling price equals production costs.

ENGR 112 HOMEWORK #4 WINTER TERM

This assignment is to be completed in a spreadsheet (EXCEL or OpenOffice CALC).

Problem #1. Graph the function f(x) = 6×2 – 18x + 6 and determine the maximum and/or minimum of the function.

Problem #2. A manufacturer of electronic components can sell n thousands of a component per week at a price per thousand is p = 200 – 1.5n where n is the number of thousands. The cost of production is dollars per thousand is c = 0.2n2 – 20n + 600. Determine the total selling price and production costs in increments of n = 5 to a total of n = 50 and tabulate the data. Plot each curve, total selling price versus number of parts and production cost versus number of parts, on the same graph.

Determine the break-even point, where selling price equals production costs.

Determine the number of parts to be manufactured that will give the largest profit.

Problem #3.Plot the following points. Then decide whether the curve can be approximated by an equation of the form y = bemx by replotting the points using a semilog plot. If so determine the points that fit the curve.

x y
0 1.8
0.2 3.6
0.4 7.3
0.6 14.7
0.8 29.6
1.0 59.6

Problem #4. Plot the following data points. Then decide whether the curve can be approximated by an equation of the form y = bxm by replotting the points on a log-log plot. If so, determine the equation that fits the points.

x y
1.0 2.2
2.0 15.3
5.0 47.7
7.0 107
10.0 199
20.0 332
50.0 511
70.0 743
100.0 1104
Problem #5. The displacement and force data below can be calculated from a stress-strain curve of a given material and a graph can be produced. The area under this curve represents the work done on the sample by the testing equipment. Use the numerical integration technique to estimate the work done on the sample.

Displacement (mm) Force (N)
0.00 0
0.12 538
0.24 1076
0.36 1614
0.48 2152
0.56 2511
0.68 3049
0.80 3334
1.40 4479
2.08 5229
3.16 5708
4.96 5979
6.68 6010
8.48 5958
10.56 5750
12.00 5542

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