(a) A necklace start-up makes profit, 7, in dollars according to the following function of the number of necklaces, q, that they sell: * = 360q - 3q'. What is the optimal number of necklaces for this firm to sell, to make the most profit? (b) Suppose the same firm realizes they must pay $ 120 dollars to open a PO box plus 12 dollars per necklace to ship necklaces to their customers; how many necklaces should they now decide to sell (assuming they cannot change their prices)? Healthcare Spending per capita vs. Average Life Expectancy Among OECD Countries 85 Japan 80 S. Korea . Average Life Expectancy at Birth (Years) UK USA Mexico . Hungary cccc= Linear Trend line 79 1000 2000 3000 4000 5000 6000 7000 Total Expenditure on Health per capita in USD26. Write an equation for the linear trend line depicted in the graph above. Presume the line hits the following two points: ($3000, 80 years) and ($1000, 76 years). 3 27. Interpret and explain the significance of the USA point on the graph above. What does it mean when compared to the other points and the trend line? 28. The United States emitted 20 metric tons of carbon dioxide per person in 1999 and 15 metric tons per person in 2019. China emitted 2.5 metric tons of CO2 per person in 1999 and emitted 7.5 metric tons per person in 2019. Write a linear equation for each country (metric tons of CO2 per person, C, on the y-axis, and time, t, on the x-axis. Assume 1999 is t = (). Based on your linear equations: in what year will the United States and China emit the same amount of CO2 per person? (a) United States' equation of a line: (b) China's equation of a line: (c) In what year are the lines equal?Find the derivative with respect to x: 13. y = -2x- - 5x + 22 16. y = 6x1 - 2x' + x +9 14. y = 27xi - 7x2 + x +9 17. y = 2+ 312 - 18 15. y = 4x3 - 7x + 15 18. y = 205-4 + 135 Find the local maximum or minimum (both the x and y coordinates), then state whether it is a local maximum or a local minimum: 19. y = 18x - 3x2 - 10 22. y = 12x2 + 24x - 100 20. y = 7x- + 56x - 100 23. y = 10 - x2 21. y = 42 + 8 - x2 24. y = 360 - 72x - 612