= a - bp₁ + dp2 2 = a - bp₂ + dp₁, here a, b > 0 and |d| < b. d > 0 indicates the products are substitutes, d < 0 indicate complements. The costs of the firms is given by (qi) = c¡qi, i = 1, 2. Profits are given by: =(P₁; Pj) = (a − bp₁ + dp;)(p; — c₁), i = 1, 2. ou are asked to perform the following tasks: 1. Build in Python a demand function that has prices, and demand parameters (a, b, d) as inputs. The function should return the quantity demanded for a given firm. 2. Build in Python a cost function that returns the cost that a given firm would incur to produce a certain quantity of output (the inputs should be quantity and the cost paramter). 3. Build in Python a profit function that returns the profit of a given firm. The user of the function should be able to choose the cost parameter, the price of the firm, the price of the competitor, and the demand parameters. 4. Build in Python a best response function that returns the optimal price of a firm, given cost, the demand parameters, and the competitor's price.

Portfolio manager Max Gaines needs to develop an investment portfolio for his clients who are willing to accept a moderate amount of risk. His task is to determine the proportion of the portfolio to invest in each of the five mutual funds listed below so that the portfolio maximizes the expected return but provides an annual return of no less than 3%. for each of the following scenarios. Annual Returns (Planning Scenarios): mutual fund yr 1 yr 2 yr 3 yr 4 international stock 22.37 26.73 6.46 -3.19 low-cap blend 14.88 18.61 10.52 5.25 mid-cap blend 19.45 18.04 5.91 -1.94 small-cap blend 13.79 11.33 -2.07 6.85 intermediate bond 7.29 8.05 9.18 3.92 Formulate the appropriate linear program for this situation. (state the objective function, the decision variables, and the constraints)

The tableau is not optimal for either maximization or a minimization problem. Thus, when a nonbasic variable enters the solution it can either increase or decrease Z or leave it unchanged, depending on the parameters of the entering nonbasic variable.     Basic          Z       0         -5       0        4        -1     -10      0        0           598           0         3        0        -2       -3      -1        5       1             12        0         1        1         3        1        0        3       0              6        1        -1        0         0        6       -4       0        0             0     Categorize the variables as basic and nonbasic and provide the current values of all the variables.                              AP [8]                  Assuming that the problem is of the maximization type, identify the nonbasic variables that have the potential to improve the value of If each such variable enters the basic solution, determine the associated leaving…

1. Let S = {1,2...n} be a set activities, where activity i € S has a start time si, a finish time f; and a profit p, asSociated with it. Design an dynamic programming algorithm for computing a set of compatible activities of maximum profit. Argue that the time complexity of you algorithm is O(n log(n)). (You must start with the correct definitions, and then write a recurrence relation.)