Question

For each function, find the indicated derivative:

a. y = x / eⁿⁿx; y''' = ?
b. f(x) = 2x⁷ - 9x⁴ + 5x + 3 / x²; f⁽⁴⁾(x) = ?
c. eⁿⁿx

Answer 1

To maximize the weekly profit, a linear programming technique such as the Simplex Method can be used to determine the optimal quantity of each type of ski.

Step-by-step explanation:

To maximize the weekly profit, we need to determine how many of each type of ski should be made. Let's assume that x represents the number of downhill skis and y represents the number of cross-country skis.

We have the following constraints:

• Manufacturing time constraint: 1x + 2y <= 16 (since manufacturing time for each type of ski is given)
• Finishing time constraint: 7x + 5y <= 49 (since finishing time for each type of ski is given)
• Non-negative constraint: x >= 0 and y >= 0 (we cannot have negative quantities)

The objective function for weekly profit is given by: P = 64x + 89y.

We can solve this problem using a linear programming technique, such as the Simplex Method. The optimal solution will provide the values of x and y that maximize the weekly profit.