Question refer to the following information.S(P) = 1/2 P + 40D(P) = 22...
Choice B is correct. The quantity of the product supplied to the market is given by the function S(P) = 1/2 P + 40. If the price P of the product increases by $10, the effect on the quantity of the product supplied can be determined by substituting P + 10 for P as the argument in the function. This gives S(P + 10) = 1/2(P + 10) + 40 = 1/2P + 45, which shows that S(P + 10) = S(P) + 5.
Therefore, the quantity supplied to the market will increase by 5 units when the price of the product is increased by $10.
Alternatively, look at the coefficient of P in the linear function S. This is the slope of the graph of the function, where P is on the horizontal axis and S(P) is on the vertical axis. Since the slope is 1/2, for every increase of 1 in P, there will be an increase of 1/2 in S(P), and therefore, an increase of 10 in P will yield an increase of 5 in S(P).
Choice A is incorrect. If the quantity supplied decreases as the price of the product increases, the function S(P) would be decreasing, but S(P) = 1/2P + 40 is an increasing function. Choice C is incorrect and may be the result of assuming the slope of the graph of S(P) is equal to 1. Choice D is incorrect and may be the result of confusing the y-intercept of the graph of S(P) with the slope, and then adding 10 to the y-intercept.
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Question refer to the following information.S(P) = 1/2 P + 40D(P) = 22...
Explanation:
To find out how the quantity of the product supplied will change if the price is increased by $10, we need to determine the new quantity supplied after the price increase.
The supply function is given by S(P) = 1/2P. This means that the quantity supplied (S) is equal to half of the price (P).
Let's consider the initial price of the product as P1. The quantity supplied at this price can be calculated using the supply function: S(P1) = 1/2P1.
Now, if the price is increased by $10, the new price becomes P1 + $10. We can calculate the new quantity supplied using the supply function: S(P1 + $10) = 1/2(P1 + $10).
To determine the change in quantity supplied, we need to find the difference between the new quantity supplied and the initial quantity supplied:
Change in quantity supplied = S(P1 + $10) - S(P1)
Now, substitute the supply function values:
Change in quantity supplied = 1/2(P1 + $10) - 1/2P1
To simplify the expression, we can distribute the 1/2 factor:
Change in quantity supplied = 1/2P1 + 1/2($10) - 1/2P1
The P1 terms cancel out, and we are left with:
Change in quantity supplied = 1/2($10)
Simplifying further:
Change in quantity supplied = $5
Therefore, the quantity supplied will increase by 5 units if the price of the product is increased by $10.
Hence, the correct answer is option B - The quantity supplied will increase by 5 units.
Question refer to the following information.S(P) = 1/2 P + 40D(P) = 22...
Choice B is correct. The quantity of the product supplied to the market is given by the function S(P) = 1/2 P + 40. If the price P of the product increases by $10, the effect on the quantity of the product supplied can be determined by substituting P + 10 for P as the argument in the function. This gives S(P + 10) = 1/2(P + 10) + 40 = 1/2P + 45, which shows that S(P + 10) = S(P) + 5.
Therefore, the quantity supplied to the market will increase by 5 units when the price of the product is increased by $10.
Alternatively, look at the coefficient of P in the linear function S. This is the slope of the graph of the function, where P is on the horizontal axis and S(P) is on the vertical axis. Since the slope is 1/2, for every increase of 1 in P, there will be an increase of 1/2 in S(P), and therefore, an increase of 10 in P will yield an increase of 5 in S(P).
Choice A is incorrect. If the quantity supplied decreases as the price of the product increases, the function S(P) would be decreasing, but S(P) = 1/2P + 40 is an increasing function. Choice C is incorrect and may be the result of assuming the slope of the graph of S(P) is equal to 1. Choice D is incorrect and may be the result of confusing the y-intercept of the graph of S(P) with the slope, and then adding 10 to the y-intercept.