Organizers of an Internet training session will charge participants $50 to atten

Question

Organizers of an Internet training session will charge participants $50 to attend if the enrollment for the session is less than 40 students. If the enrollment is 40 or more students (per session) the fee is $40 per student.. It costs 8500 to reserve the room, pay the instructor, use the equipment, and advertise. The cost for printing course materials is 830 per student for the organizers. If (a) Develop an expression for the total cost to the organizers. (b) Develop an expression for the total revenue to the organizers. (c) Graph both the cost and revenue functions on the grid below. Shade and label regions of loss and profit. (d) Name the range(s) of students for which the company will be making a profit.

Explanation / Answer

a)

let x be number of students enrolled

cost = 500 + 30*x

b) revenue = {50 x*   if x < 40

                       40*x          if x >= 40

c)

d)

Profit when x = 25 to 39

and when n >= 51

Please rate my solution

No. of students Revenue Cost profit 0 0 500 -500 1 50 530 -480 2 100 560 -460 3 150 590 -440 4 200 620 -420 5 250 650 -400 6 300 680 -380 7 350 710 -360 8 400 740 -340 9 450 770 -320 10 500 800 -300 11 550 830 -280 12 600 860 -260 13 650 890 -240 14 700 920 -220 15 750 950 -200 16 800 980 -180 17 850 1010 -160 18 900 1040 -140 19 950 1070 -120 20 1000 1100 -100 21 1050 1130 -80 22 1100 1160 -60 23 1150 1190 -40 24 1200 1220 -20 25 1250 1250 0 26 1300 1280 20 27 1350 1310 40 28 1400 1340 60 29 1450 1370 80 30 1500 1400 100 31 1550 1430 120 32 1600 1460 140 33 1650 1490 160 34 1700 1520 180 35 1750 1550 200 36 1800 1580 220 37 1850 1610 240 38 1900 1640 260 39 1950 1670 280 40 1600 1700 -100 41 1640 1730 -90 42 1680 1760 -80 43 1720 1790 -70 44 1760 1820 -60 45 1800 1850 -50 46 1840 1880 -40 47 1880 1910 -30 48 1920 1940 -20 49 1960 1970 -10 50 2000 2000 0 51 2040 2030 10 52 2080 2060 20 53 2120 2090 30 54 2160 2120 40 55 2200 2150 50 56 2240 2180 60 57 2280 2210 70 58 2320 2240 80 59 2360 2270 90 60 2400 2300 100

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