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Use Table 1 to evaluate all
75. Cost. A company manufactures downhill skis. It has fixed costs of $25,000 and a marginal cost given by
where C(x) is the total cost at an output of x pairs of skis. Find the cost function C(x) and determine the production level (to the nearest unit) that produces a cost of $150,000. What is the cost (to the nearest dollar) for a production level of 850 pairs of skis?
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- 18. Suppose that a company produces and sells bicycles and that the start-up cost is $3000 and $75 for each bike produced. The function, C), gives the average cost of producing 5000 +35x C(x)= %3Darrow_forward. A calculator company found that the cost of producing x graphing calculators per day isC(x) = 4x + e^0.02x.(This ignores the original research and development cost, which is quite large.)(a) If each calculator is priced at $80, find a revenue function, R(x), which gives the revenuefor x calculators sold.(b) Find the profit function, P(x), which gives the profit per day when x calculators areproduced and each later sold for $80.(c) Find the value of x that will maximize P(x). Use the second derivative test to show thatit yields a maximum.(d) Given that one cannot produce a fraction of a calculator, find the daily production levelthat will maximize profit. Please answer in a complete sentence.arrow_forwardSuppose the marginal cost of producing x units of a product is given by: MC=30 Square root (x+4) And the marginal revenue is given by: MR = 900 And the fixed costs are $1000. What is the profit (or loss) for the production and sale of 5 units of this product ? How many units are needed to be sold to make the maximum profit?arrow_forward
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- A poster consists of a printed area and margins(See image). The area of the entire poster is A = 600 square inches. The goal is to find the dimensions and y that maximizes the printed area. A = 3" The area of the printed part, as a function of x and y is Now, A'(x) = X = y = Use the substitution principle to rewrite the area as a function of x. Hint: You are given the area of the total poster. A = A(x) = To determine optimal values, we need to look at A'(x) = 0. Solving for x and, ultimately for y, yields inches inches 2" X O 2" one ore. te y What is the maximum area of the printed part? A = C 3" square inchesarrow_forward9. Create the equation of a polynomial function where the instantaneous rate of change is equal to 0 when x = 1 and when x = 3, and that the instantaneous rate of change is negative if x < 1.arrow_forwardIf TC=0.01x²+5x+100 is the cost function for x items of a product, at what level of production, x is there minimum average cost? What is the minimum average cost?arrow_forward
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