# Set of math questions need to be solved. Nothing fancy and show your work please.

Anonymous

### Question Description

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) = 0.0004x3 - 0.036x2 + 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)

1

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 - 0.02x2 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) = 9x3 + 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)

### Unformatted Attachment Preview

Name___________________________________ Math 145-201 Exam #3 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) = 0.0004x3 - 0.036x2 + 200x + 40,000 1) R(x) = 450x Solve the problem. 2) The demand equation for a certain item is p = 14 - x and the cost equation is C(x) = 1,000 2) 7,000 + 4x. Find the a) revenue function and b) marginal profit at a production level of 3,000 and interpret the result. 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. 1 4) 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 5) of p for which demand is inelastic.. Solve the problem. 6) The annual revenue and cost functions for a manufacturer of zip drives are approximately R(x) = 520x - 0.02x2 and C(x) = 160x + 100,000, where x denotes the 6) number of drives made. What is the maximum annual profit? 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. Find where the following function is increaseing and decreasing. 8) f(x) = x 3 - 4x 2 7) 8) Determine where the given function is concave up and where it is concave down. 9) q(x) = 9x3 + 2x + 5 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 y= 9) 10) 6x x2 + 1 Repeat the directions from the problem above for the following equation. 11) y = 5x + 9 . 11) 3 Name___________________________________ Math 145 Practice Problems- Marginal Analysis & Elasticity of Demand Provide an appropriate response. 1) Suppose that the total profit in hundreds of dollars from selling x items is given by P(x) =4x2 5x + 10. Find the marginal profit at x = 5. A) \$35 B) \$45 C) \$15 D) \$32 1) Solve the problem. 2) The demand equation for a certain item is p = 14 - x and the cost equation is C(x) = 7,000 + 1,000 2) 4x. Find the marginal profit at a production level of 3,000 and interpret the result. A) \$14; at the 3,000 level of production, profit will increase by approximately \$14 for each unit increase in production. B) \$7; at the 3,000 level of production, profit will increase by approximately \$7 for each unit increase in production. C) \$16; at the 3,000 level of production, profit will increase by approximately \$16 for each unit increase in production. D) \$4; at the 3,000 level of production, profit will increase by approximately \$4 for each unit increase in production. Find the elasticity of the demand function as a function of p. 3) x = D(p) = 700 - p p 1 A) E(p) = B) E(p) = 2p - 1400 1400 - 2p C) E(p) = p 700 - p D) E(p) = 3) p 1400 - 2p Use the price-demand equation to determine whether demand is elastic, is inelastic, or has unit elasticity at the indicated values of p. 4) x = f(p) = 2005 - p2; p = 13 4) A) Elastic B) Inelastic C) Unit elasticity Use the price-demand equation to find the values of p which meet the given condition of elasticity. 5) x = f(p)= 246 - 8p; determine the values of p for which demand has unit elasticity. Round to two decimal places if necessary. A) Inelastic at p = 31.36 B) Inelastic at p = 15.38 C) Inelastic at p = 15.68 D) Inelastic at p = 7.69 1 5) Answer Key Testname: PRACTICE PROBLEMS- MARGINAL ANALYSIS & ELASTICITY OF DEMAND 1) A 2) D 3) D 4) B 5) B 2 Name___________________________________ Math 145 Practice Problems- Optimization Solve the problem. 1) 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. A) 57.6 ft @ \$8 by 14.4 ft @ \$4 C) 40.7 ft @ \$8 by 20.4 ft @ \$4 1) B) 20.4 ft @ \$8 by 40.7 ft @ \$4 D) 14.4 ft @ \$8 by 57.6 ft @ \$4 2) Find the dimensions that produce the maximum floor area for a one-story house that is rectangular in shape and has a perimeter of 139 ft. A) 34.75 ft × 139 ft B) 11.58 ft × 34.75 ft C) 34.75 ft × 34.75 ft D) 69.5 ft × 69.5 ft 2) 3) From a thin piece of cardboard 10 in. by 10 in., square corners are cut out so that the sides can be folded up to make a box. What dimensions will yield a box of maximum volume? What is the maximum volume? Round to the nearest tenth, if necessary. A) 5 in. by 5 in. by 2.5 in.; 62.5 in.3 B) 3.3 in. by 3.3 in. by 3.3 in.; 37 in.3 3) C) 6.7 in. by 6.7 in. by 3.3 in.; 148.1 in.3 D) 6.7 in. by 6.7 in. by 1.7 in.; 74.1 in.3 1 Answer Key Testname: PRACTICE PROBLEMS- OPTIMIZATION 1) B 2) C 3) D 2 ...
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