An artisan produces two types of handmade surfboards - the competitive model and

Question

An artisan produces two types of handmade surfboards - the competitive model and the standard model. The graph shows several contours of the function P(c, s), the weekly profit in dollars from the sale of c competitive and s standard surfboards. a. Find and interpret P(2, 4), the point shown on the graph. b. Is P increasing more rapidly as c increases or as s increases at the point (2, 4)? c. When 8 competitive surfboards and 4 standard surfboards are sold weekly, is P increasing as c decreases or s decreases? d. Fill in values in the blanks. P(7, 2) = P(8, 4) = P(4, 6) = P(3, 2) = e. Write more than, less than, or about the same as in the blank: The change in the weekly profit when the point (7, 2) moves to the point (8, 4) is the change in the profit when the point (4, 6) moves to the point (3, 2).

Explanation / Answer

a) The point P(2,4) 760. That means the artisan will get approximately 760 units of profit by selling 2 competitive and 4 standard surfboards.

b) P is increasing more rapidly as c increases as normal to the curve at (2,4) is in the +ve x direction.

c) At (8,4) P is increasing as s decreases because our point will move from P=1060 curve to P=1110 curve.

d) P(7,2) 960 , P(8,4) 1060, P(4,6)910, P(3,2) (860+910)/2 = 885

e) P(8,4) - P(7,2) = 100 and P(4,6) - P(3,2) = 25

the change is more than.

DO THUMBS UP ^_^

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