Answer:
zero goats and 120 Ilamas to get profit of $15,120
Step-by-step explanation:
Goats: G
Ilamas: l
Explicit constraints:
2G + 5l ≤ 400
100G+ 80l≤ 13,200
Implicit constraints
G≥0
I≥0
P= 84G+ 126l
See attachment for optimal area
substituting coordinats of optimal region in profit equation to get profit
When G= 132, l=0
P=84(132) + 126(0)
P=11,088
When G=0, l=120
P=84(0)+ 126(120)
P = 15120
When G= 100, l=40
P=84(100)+126(40)
P=13440
Answer:
56√93 ≈ 540 ft²
Step-by-step explanation:
The roof is made up of 4 congruent isosceles triangles. Since the roof extends 2 ft over the edge of the cottage on each side, then the base of each triangle is 26 + 2 = 28 ft.
Let's calculate the area of one of the triangles and then just multiply by 4. See attachment. Drop a perpendicular from the vertex of a triangle to its base. We now have the triangle broken up into two right triangles. The hypotenuse is 17 ft and one of the legs of the right triangle is 28 / 2 = 14 ft. Then the height / other leg is:
We now have the dimensions of each triangle: the height is √93 and the base is 28. The area of a triangle is: A = (1/2) * b * h, so we have the following.
A = (1/2) * b * h
A = (1/2) * 28 * √93 = 14√93
Multiply this by 4:
14√93 * 4 = 56√93
The total surface area is 56√93 ≈ 540 ft².
