Word Problem Linear progrmming

Question

According to FBI's, "Global Information System Security 2015", there were 3.4 million “detected and reported information security incidents” (cyberattacks, etc.) against computer networks in the USA in 2009. In 2014, that number had risen to 42.8 million.
(a) Which of the following linear equations could be used to predict annual number (in millions) of detected and reported information security incidents “y” in a given year “x”, where x = 0 represents the year 2009? Explain/show work.
??. ??=7.88??+2009 ??. ??= 0.13??+2009 ??. ??=7.88??+3.4 ??. ??= 0.13??+3.4
(b) Use the equation from part (a) to predict the number (in millions) of detected and reported information security incidents in the year 2024. Round answer to nearest tenth of a million. Show work.
(c) Fill in the blanks to interpret the slope of the equation: The rate of change of detected and reported information security incidents against computer networks in the US with respect to time is __________ per ___________. (Include units of measurement.)

Answer 1

This contrived problem is neither a linear programming problem nor an appropriate use of estimating techniques (since the curve is clearly far from linear).  (But it is a SWAG) So, let’s assume a different subject so we can concentrate on the math.  Given:
    At  x=0    y=3.4M                    This is point P₀:  (0,3.4)
    At  x=5    y=42.8M                  This is point P₁:  (5,42.8)

(a) The formula for a line when given two points is:
                           (y – y₀)(x₁ – x₀) = (y₁ – y₀)(x –x₀)

   So,
                             (y-3.4)(5-0) = (42.8-3.4)(x-0)
                                  5y = 39.4x + 17.0          (collect terms)
                                   y = 7.88x + 3.4       (divide by 5)

(b) In 2024, the value is x=15.  Calculate y:
                                   y = 7.88(15) + 3.4
                                   y = 121.6

(c) The slope is (y₂ – y₁) / (x₂ – x₁) 
                            = (42.8 – 3.4) / (5 – 0)
                            = 39.4 / 5
                            = 7.88 million per year