In: Advanced Math
A company manufactures and sells scientific calculators. The function P=7.87.8x2plus+59705970xminus−290 comma 000290,000, x≤150, gives the profit if x thousand calculators are manufactured and sold. Use the table feature of a graphing calculator or use a spreadsheet to make a table of values for the profit function with x=0, 5, 10, ..., 150. Use the table to answer the following question.
Approximately how many calculators must be sold in order for the company to make a profit?
x in 1000's | Profit |
0 | -2,90,000 |
5 | -2,59,955 |
10 | -2,29,520 |
15 | -1,98,695 |
20 | -1,67,480 |
25 | -1,35,875 |
30 | -1,03,880 |
35 | -71,495 |
40 | -38,720 |
45 | -5,555 |
50 | 28,000 |
55 | 61,945 |
60 | 96,280 |
65 | 1,31,005 |
70 | 1,66,120 |
75 | 2,01,625 |
80 | 2,37,520 |
85 | 2,73,805 |
90 | 3,10,480 |
95 | 3,47,545 |
100 | 3,85,000 |
105 | 4,22,845 |
110 | 4,61,080 |
115 | 4,99,705 |
120 | 5,38,720 |
125 | 5,78,125 |
130 | 6,17,920 |
135 | 6,58,105 |
140 | 6,98,680 |
145 | 7,39,645 |
150 | 7,81,000 |
For X=45.832, Profit(P)=0
So the company has to manufacture and sell minimum of 45,832 calculators to make profit.