Answer:
To minimize the cost, the Chicago plant should run 30 days and the Detroit plant should run 20 days.
Step-by-step explanation:
This is a linear programming question, in which there is a function to optimize (minimize cost) and restrictions, all linear functions.
The objective function is Cost:
C: cost function
H: days of operation for Chicago plant
D: days of operation for Detroit plant
The restrictions are:
- Minimum requirements for radial tires:
- Minimum requirements for standard tires:
- Days are positive integers
We have 3 points in which 2 of the constraints are saturated. In one of this three points is the minimum cost.
We will evaluate them to find the minimum cost:
Point 1: H=0, D=80
Point 2: H=50, D=0
Point 3: H=30, D=20
The third point minimizes the cost.
To minimize the cost, the Chicago plant should run 30 days and the Detroit plant should run 20 days.
Answer:
8.75+7.45=16.2. 16.2 is equal to $16.20 so 48.00-16.20=31.8. Jonathan had $31.80 left.
Step-by-step explanation:
Answer:
AA Postulate
Step-by-step explanation:
The bottom lines are parallel. In this case they are also congruent. Combined with the top angle this makes in AA postulate
Answer:
answe is 1+i
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Answer:
Area: 272ft²
Volume = 82.6236447189ft³
Step-by-step explanation:
AREA
The area of a square pyramid is found by combining the area of the base and the area of the triangular faces:
Area of base = area of square = L² = 8² = 16ft²
Area of one triangular face = (1/2)bh = (1/2)(8)(16) = 64ft²
There are four triangular faces so the total area = 16+4(64)= 16+256= 272 ft²
VOLUME
The volume of a square pyramid = (a²)(h/3), where a is the length of the base and h is the length from the top of the pyramid to the middle of the square.
We are given a, but not h. To find h, we must imagine a right-angled triangle within the pyramid, where 16ft is the hypotenuse, h is the height and the base is half of a (since the base is a square and the distance is from the edge to the middle). We can then use pythagorus's theorem to find h:
A²=B²+C²
16²=(8/2)²+h²
256=16+h²
h=√240
h=15.4919333848ft
Knowing h, we can find the volume:
Volume = (a²)(h/3)
Volume = (8²)(15.4919333848/3)
Volume = (16)(5.16397779493)
Volume = 82.6236447189ft³
