Provide an appropriate response. 1)Let C(x) be the cost function and R(x) the revenue function. Compute the marginal cost, marginal revenue, and the marginal profit functions. C(x) = 0.0004×3 – 0.036×2 + 200x + 40,000 R(x) = 450x
1)
Solve the problem. 2)The demand equation for a certain item is p = 14 – x 1,000 and the cost equation is C(x) = 7,000 + 4x. Find the a) revenue function and b) marginal profit at a production level of 3,000 and interpret the result.
2)
Use the price-demand equation to determine whether demand is elastic, inelastic, or unitary at the indicated values of p. 3)x = f(p) = 276 – 4p; p = 48. 3)
4)How is revenue effected for the problem above (increase, decrease, stays the same)? Explain.
4)
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Use the price-demand equation to find the values of p which meet the given condition of elasticity. 5)x = f(p) = 216-2p2; determine the values of p for which demand is elastic and the values of p for which demand is inelastic.. 5)
Solve the problem. 6)The annual revenue and cost functions for a manufacturer of zip drives are approximately R(x) = 520x – 0.02×2 and C(x) = 160x + 100,000, where x denotes the number of drives made. What is the maximum annual profit?
6)
7)A rectangular field is to be enclosed on four sides with a fence. Fencing costs $8 per foot for two opposite sides, and $4 per foot for the other two sides. Find the dimensions of the field of area 830 ft2 that would be the cheapest to enclose.
7)
Find where the following function is increaseing and decreasing. 8)f(x) = x3 – 4x 8)
2
Determine where the given function is concave up and where it is concave down. 9)q(x) = 9×3 + 2x + 5 9)
10)Graph the following equation and provide information on a) vertical asymptotes, b) horizontal asymptotes, c) intercepts, d) critical numbers,e) where the function is increasing/decreasing, f) inflection points, g) concavity, h) any min/max
10)
y = 6x x2 + 1
Repeat the directions from the problem above for the following equation. 11)y = 5x + 9 . 11)
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