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Unformatted text preview: MGSC 1206.2 Assignment #6  SOLUTIONS Winter 2008 Due: 1 pm, Friday, March 14 th TOTAL MARKS FOR THIS ASSIGNMENT = 85 Note: Points will be deducted if you do not (a) show your work including suitable calculations, (b) use proper notation, and (c) answer word problems with words. Hand in your answers to the following seven questions: 1. Textbook 12.3 #58 (p.703) 1 2 pts 2 pts. could be 10000x(2/3)x 3 2 pts 2 pts 2 pts 2 pts 2. Textbook 13.1 #36 (p.737) 3. Textbook 13.1 #20 (p.737) 2 2 pts 2 pts 1 pt 2 pts 1 pt 2 pts 3 pts 4. Textbook 13.2 #36 (p.751) 5. Yearly demand for the Vigo Turbot automobile can be described by the demand function p x x ( ) , = 10 000 5 where x represents the quantity sold and p(x) represents the price in dollars. Total production cost to produce x vehicles is c x x x x ( ) , , = + + 3 2 140 7 000 100 000. a) Determine the revenue function R(x). Revenue = price*quantity R(x) = p(x)*x = (10,000 – 5x)x = 10,000x – 5x 2 3 1 pt 2 pts 1 pt 1 pt 1 pt 3 pts. To verify, can refer to the shape of a quadratic, as above  or better, use the First Derivative Test (or 2 nd Deriv Test) b) Determine the revenue when 200 vehicles are sold. R(200) = 10,000(200) – 5(200) 2 = $1,800,000 The total revenue will be $1,800,000 c) Determine the marginal revenue when 200 vehicles are sold. Marginal Revenue = R’(x) = { } 2 5 000 , 10 x x dx d = 10,000 – 10x At x = 200, R’(200) = 10,000 – 10(200) = $8,000 The marginal revenue from selling one more vehicle is approximately $8,000. d) Determine the marginal cost when 200 vehicles are sold. Marginal Cost = C’(x) = { } 000 , 100 000 , 7 140 2 3 + + x x x dx d = 3x 2 – 280x + 7,000 At x = 200, C’(200) = 3(200) 2 – 280(200) + 7000 = $71,000 The marginal cost of making one more vehicle is $71,000! e) Determine whether it would it be wise to produce exactly 200 vehicles, or more, or less. If 200 vehicles was the right number to produce, we would have marginal revenue equal to marginal cost, but that is not the case. At a production of 200 vehicles, the marginal cost (71,000) is far greater than the marginal revenue (8,000) so we will be losing money on any additional vehicles. We should make less because reducing production even by one will cut costs by much more than we would cut revenues. production even by one will cut costs by much more than we would cut revenues....
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 Spring '11
 Jang
 Derivative

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