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- A firm can produce only 3200 units per month. The monthly total cost is given by C(x) = 500 + 200x dollars, where x is the number produced. If the total revenue is given by 1 R(x) = 450x − ------- x^2 100 dollars, how many items, x, should the firm produce for maximum profit? x=____ Find the maximum profit. $____The total daily profit (in thousands of pesos) of a certain food company for the sale of x boxes of buko pie is given by the profit function P(x)=-0.001x^3+0.1x^2+3x-300 , where x is greater than or equal to 0 but less than or equal to 30. Determine the number of boxes of buko pie to be produced in order for the company to realize a maximum profit.How did you get g= -3 and f=2 in the first given? Kindly show solution
- A company has installed new machinery that will produce a savings rate (in thousands of dollars per year) ofS′(x) = 225 - x2,where x is the number of years the machinery is to be used. The rate of additional costs (in thousands of dollars per year) to the company due to the new machinery is expected to beC′(x) = x2 + 25x + 150.For how many years should the company use the new machinery? Find the net savings (in thousands of dollars) over this period.The revenue from the sale of x door snakes is given by R(x)=45x−0.3 dollars. The total cost is given by C(x)= .1x^2 -7x+690 dollars, where 0≤x≤100. Determine the interval of sales for which the profit is increasing and the interval for which it is decreasing. Express your answer in open intervals.On the interval -4 < x < -3, the function is… •maximum •minimum •increasing •decreasing •constant