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 = ax + b + c, where y represents the profit in thousands of pounds) the company is predicted to make, and I represents the amount of fudge (in tonnes) produced in the year. The values of a, b and c are 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 +5.8251 +9.215. By considering the coefficient of r, 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=-15.217.r+ 18.379 - -0.829. In this part of the question, you are asked to consider the parabolic graph modelled by the equation y = -15.217.22 +18.379.2 -0.829. (i) 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. (iii) Use the quadratic formula to find the r-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. 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 = ax + b + c, where y represents the profit in thousands of pounds) the company is predicted to make, and I represents the amount of fudge (in tonnes) produced in the year. The values of a, b and c are 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 +5.8251 +9.215. By considering the coefficient of r, 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=-15.217.r+ 18.379 - -0.829. In this part of the question, you are asked to consider the parabolic graph modelled by the equation y = -15.217.22 +18.379.2 -0.829. (i) 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. (iii) Use the quadratic formula to find the r-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
