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- A chemical manufacturer sells sulfuric acid in bulk at a price of $100 per unit.If the daily total production cost in dollars for x units isC(x) = 100, 000 + 50x + 0.0025x2and if the daily production capacity is at most 7000 units.(a) How many units of sulfuric acid must be manufactured and sold daily tomaximize the profit? (b) Would it benefit the manufacturer to expand the daily production capacity?A firm producing poultry feed finds that the total cost C(x) in dollars of producing and selling x units is given by C(x)=20x+100Management plans to charge $24 per unit for the feed.The revenue at the break-even point is$5. A fast food restaurant has a cost of production C (x) = 14x + 171 and a revenue function R(x) = 5x. When does the company begin to turn a profit?
- Eliminate the arbitrary constants from the following equations. x2 = axy + byFind the general solution to x”-3x’+2x = e^t??????? ? (a) (i) Lim 5x −3 − 4/ 2x −2 + 9 x→∞ (ii) Lim (x − 3) 2/x2/2 − 2x − 3 x→∞ During a nationwide program to immunize the population against a new strain of the flu, public health officials determined that the cost of inoculating x% of the susceptible population would be approximately C(x) = 1.85x/100 - x million dollars. (i) What would it cost to providing immunization to the first 20% of the susceptible population? (ii) What would it cost to providing immunization to the next 30% of the susceptible population? (iii) Suppose 17 million dollars are available for providing immunization. What percentage of the susceptible population will not receive immunization? (iv) If money was not a problem will they be able to providing immunization to the entire susceptible population? (c) Determine the values of x for which the function f(x) = {2x2 – 4 x < 2 {x + 2 2 < x > 5 {7 x ≥ 5 is…
- Find a quadratic equation for a function y=f(x) which crosses the x-axis at x=5 and x=6, and which crosses the y-axis at y=-60. What would f(x) equal?There is a part B to this question and it isSolve R(x)>C(x) [algebraically, graphically, or numerically] and explain what this means in terms of cups of lemonade sold.Find f by solving the initial-value problem. f '(x) = 9x2 + 8x − 5; f(2) = 2