The number of portable CD players you are prepared to supply to a retail outlet every week is given by the formula:
q = 0.1p2 + 2p
where p is the price it offers you. The retail outlet is currently offering you $50 per CD player. If the price it offers decreases at a rate of $1 per week, how will this affect the number you supply?
q = 0.1p^2 + 2p
dq/dt = (0.2p + 2) dp/dt
at p=50,
dq/dp = (10+2)(-1) = -12
so the number supplied is decreasing by 12 per week.
Well, well, well... Looks like we've got an equation maker here! Let's crunch those numbers, shall we?
According to the formula q = 0.1p^2 + 2p, where p is the price they offer you, we can substitute their current offer of $50 per CD player into the equation:
q = 0.1(50)^2 + 2(50)
q = 0.1(2500) + 100
q = 250 + 100
q = 350
So, currently, you are supplying them with 350 portable CD players every week.
Now, if the retail outlet decides to decrease the price by $1 per week, we can track how it affects the number you supply. Let's go step by step, my friend:
Week 1: Price = $49, substitute it into the equation
q = 0.1(49)^2 + 2(49)
q = 0.1(2401) + 98
q = 240.1 + 98
q ≈ 338.1
Week 2: Price = $48, substitute again
q = 0.1(48)^2 + 2(48)
q = 0.1(2304) + 96
q = 230.4 + 96
q ≈ 326.4
Week 3: Price = $47... you get the idea
By continuing this pattern, you can see that as the price decreases, the number of CD players you supply also decreases. So, it's safe to say that as the retail outlet lowers the price, your supply will decrease gradually.
Remember, my friend, economics can be a bit tricky, but with a sprinkle of humor, we can make it more fun!
To determine how the change in price offered by the retail outlet affects the number of CD players you supply, we can substitute the price into the supply equation and observe the resulting quantity.
The equation for the supply of CD players is given by:
q = 0.1p^2 + 2p
Currently, the retail outlet offers $50 per CD player. Thus, we can substitute p = 50 into the equation:
q = 0.1(50)^2 + 2(50)
q = 0.1(2500) + 100
q = 250 + 100
q = 350
Therefore, currently, you are supplying 350 portable CD players to the retail outlet every week.
Now, let's consider what happens if the price offered decreases by $1 each week. To determine the new quantity supplied, we need to substitute the new price (p - $1) into the equation for supply:
q = 0.1(p - 1)^2 + 2(p - 1)
Substituting p = 50 into the equation:
q = 0.1(49)^2 + 2(49)
q = 0.1(2401) + 98
q = 240.1 + 98
q = 338.1
Therefore, if the price offered by the retail outlet decreases by $1 each week, the number of CD players you supply will decrease to 338.1 (rounded to the nearest whole number).
To determine how the decrease in price offered by the retail outlet will affect the number of portable CD players you supply, we can substitute the different prices into the formula and observe the change in the corresponding quantity.
Let's start by calculating the number of CD players you supply at the current price offered by the retail outlet, which is $50 per CD player.
Substituting p = $50 into the formula:
q = 0.1(50)^2 + 2(50)
q = 0.1(2500) + 100
q = 250 + 100
q = 350
So, currently, you supply 350 portable CD players to the retail outlet every week.
Now, let's analyze the effect of a $1 decrease in price offered by the retail outlet per week. We will decrease the price by $1 and calculate the new quantity supplied.
Substituting p = $49 into the formula:
q = 0.1(49)^2 + 2(49)
q = 0.1(2401) + 98
q = 240.1 + 98
q = 338.1
Therefore, with a $1 decrease in price, the number of portable CD players you will supply decreases to approximately 338.1 players per week.
It is important to note that since the number of CD players supplied is continuous, the value obtained is an approximation. In practice, you would likely supply either 338 or 339 CD players.