The owner of an orange grove must decide when to pick one variety of oranges. She can sell them for $24 a bushel if she sells them now, with each tree yielding an average of 4 bushels. The yield increases by half a bushel per week for the next 5 weeks, but the price per bushel decreases by $1.50 per bushel each week. In how many weeks should the oranges be picked for maximum return?

4

Step-by-step explanation:

Let's say the amount of bushes sold (yield) is b, and the price per bushel is p.

When calculating total revenue, we want to multiply price by quantity. Quantity here is b, and price is p. Therefore, p*q = revenue = return.

Let's say that the amount of weeks is w.

Price after w weeks = 24 - 1.50 for each week = 24 - 1.50w

Yield after w weeks = 4 + 0.5 for each week = 4 + 0.5w

Revenue after w weeks = p * b = (24-1.50w) * (4+0.5w) = 96 - 6w + 12w - 0.75w² = -0.75w²+6w + 96.

We want to maximize revenue. First, we can find when the derivative of the function is 0.

d/dw(-0.75w²+6w + 96) = -1.5w + 6 = 0

subtract 6 from both sides

-1.5w = -6

divide both sides by -1.5 to isolate w

w = 4

plug that into our equation

-0.75(4)²+6(4) + 96 = -12 + 24 + 96 = 108

Because this function has a negative coefficient for the w², we can say that it is a parabola opening up downward, so when the derivative = 0, we have found the maximum of the function. Therefore, 4 is our answer

(2x + 16) + (x) = 180

step-by-step explanation:

given,

abcd is a quadrilateral inscribed in a circle

angle a is labeled x plus 16, (x + 16)

angle b is labeled x degrees, (x)

angle c is labeled 6x minus 4, (6x – 4)

angle d is labeled 2x plus 16, (2x + 16)

what equation can be used to solve for angle b?

we know that the sum of the opposite angles of a simple quadrilateral inscribed in a circle is 180 degrees.

angle b is opposite angle d

therefore, angle b + angle d = 180

(x) + (2x + 16) = 180 

same as (2x + 16) + (x) = 180