To determine the properties of this ellipse we will make use of several key features of an ellipse.
1. The semi-major axis (a): The semi-major axis is the longest radius of an ellipse, in this case, it's the distance from the center of the ellipse to the vertex. As given, the vertex is at (3,0), and since the center of the ellipse is at the origin (0,0), the length of semi-major axis 'a' is the absolute difference between the x-coordinates of the vertex and the center. So, |3 - 0| = 3.
2. The distance between the center and the focus (c): This is simply the absolute difference between the x-coordinate of the focus and the center. The focus is at (1,0) and the center is at the origin (0,0), so |1 - 0| = 1.
3. The semi-minor axis (b): The semi-minor axis is the shortest radius of an ellipse, and is perpendicular to the semi-major axis. For an ellipse, the semi-major axis, semi-minor axis, and the distance from the center to the focus are related by the equation c^2 = a^2 - b^2. So, b can be calculated by rearranging this equation to solve for b, giving b = sqrt(a^2 - c^2), and substituting the values we calculated for a and c, we get b = sqrt(3^2 - 1^2) = sqrt(9 - 1) = sqrt(8), approximately 2.83.
So, this ellipse has a semi-major axis of 3, a semi-minor axis of approximately 2.83, and the foci are located at the points (±1, 0).
Optimal Order Quantity Using EOQ Model:
The Economic Order Quantity (EOQ) model is used to calculate the most cost-effective amount to order given certain conditions.
The model's formula is: EOQ = sqrt((2 * D * S) / H)
where:
- D is the demand rate
- S is the ordering cost
- H is the holding or carrying cost per unit
Substituting the gave values into the formula, we get:
EOQ = sqrt((2 * 350 * 25) / 2) = sqrt((17500) / 2) = sqrt(8750)
To find the exact square root of 8750, you need to be familiar with simplification of square roots. However, let's find an approximate value using a calculator.
EOQ ≈ 93.54
Therefore, the pizza shop should order approximately 94 pizzas (rounded to the nearest whole number as we can't order fractional pizzas), for optimal costing according to the EOQ model.