Question

Lydia is a computer programmer for a small startup company which manufactures artisan fudge. She is creating an economic model to predict how much fudge should be produced to maximise profit in the company's first year. If too little fudge is made, the company will not meet consumer demand and will miss the opportunity to sell more. If too much fudge is made, there will be an excess of unsold fudge, which will incur a cost to the company. Lydia's computer program models the situation as a quadratic equation of the form y=ar + + where y represents the profit (in thousands of pounds) the company is predicted to make, and represents the amount of fudge (in tonnes) produced in the year. The values of a, b and care determined by the computer code, depending on various economic measures and results of market research which Lydia inputs manually. (a) Lydia wants to check that her code is working correctly. She inputs some test values and runs the code to simulate the model. The quadratic equation output by her code is y = 12.1972° +5.825x + 9.215. By considering the coefficient of 22, explain why Lydia's code must contain an error (b) Lydia corrects the error, and runs the code again. This time the quadratic equation output by the code is y = -15.217x2 + 18.3792 -0.829 In this part of the question, you are asked to consider the parabolic graph modelled by the equation y = -15.21722 +18.3798 -0.829. 6) Explain why the y-intercept is -0.829. (ii) Using the context of the question, give one possible reason why the y-intercept is negative. page 3 of 11 (iii) Use the quadratic formula to find the o-intercepts. Give your answers correct to three decimal places (iv) The chief executive officer (CEO) of the company wants to set a target of producing 1.2 tonnes of fudge in the first year. Should Lydia support or advise against this target? Explain your answer. (v) The CEO sets a target of making £4000 profit in the first year. The company decides to produce 0.4 tonnes of fudge. According to Lydia's model, will the company exceed or fall short of its target? Explain your answer.

could you please write clearly

Answer 1

solulion: According to the given data, the following la) In which, The Griven relation is, y = 12.19739755825x + 9.215 where y- probit H-) Amount & fudge Here, to solve quadratic esuation 197 art 5.825 x + 9.215=0 12 So, x -0.2388 +1 0.8358 x = -0.2388 -0.8358 since , both the values of a or amount of fudge imaginary , to lydia's Code must Contein an error.

(6) Here, the new quadratic equation is, y= -15.217 xv +18.379 x-0.829 گی 4 3 2 1 1 2 -1 ( ? ) putting azo we can get 4- incercept by I here tore, y-intercept -0.829 then probit (1) Also, it amount of fudge is zero . must be negative by putting y=0 (iii) x - inlercept we can get -15.217 x + 18.3798 -0.829=0 80, 2,- 1. 1608 1.161 x2 = 0.0409 v 0.047

(iv) on giving the advise as protit i value of xin between 0.0469 posilive, if and 1.2 > 1-16 08 Here 1. 1608 80, is negative the probit advice against this target Hence lydia , PE x=0.4 and then In which , on putting we get y = -15.217 (0:4) 4 18.37964) -0.629 24:05 788 so , tonnes of fudge probit 0.4 € 4087.88 -> which e greater than the target set by CEO Hence, according according to lydia's model. Thus, The Company exceed of its target

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