Find the minimum value of the function z=2x+2y subject to the following constraints. x≤17 y≤16 5x+2y≥42 3x+11y≥84
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Find the minimum value of the function
z=2x+2y
subject to the following constraints.
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- Although the normal distribution is a reasonable input distribution in many situations, it does have two potential drawbacks: (1) it allows negative values, even though they may be extremely improbable, and (2) it is a symmetric distribution. Many situations are modelled better with a distribution that allows only positive values and is skewed to the right. Two of these that have been used in many real applications are the gamma and lognormal distributions. @RISK enables you to generate observations from each of these distributions. The @RISK function for the gamma distribution is RISKGAMMA, and it takes two arguments, as in =RISKGAMMA(3,10). The first argument, which must be positive, determines the shape. The smaller it is, the more skewed the distribution is to the right; the larger it is, the more symmetric the distribution is. The second argument determines the scale, in the sense that the product of it and the first argument equals the mean of the distribution. (The mean in this example is 30.) Also, the product of the second argument and the square root of the first argument is the standard deviation of the distribution. (In this example, it is 3(10=17.32.) The @RISK function for the lognormal distribution is RISKLOGNORM. It has two arguments, as in =RISKLOGNORM(40,10). These arguments are the mean and standard deviation of the distribution. Rework Example 10.2 for the following demand distributions. Do the simulated outputs have any different qualitative properties with these skewed distributions than with the triangular distribution used in the example? a. Gamma distribution with parameters 2 and 85 b. Gamma distribution with parameters 5 and 35 c. Lognormal distribution with mean 170 and standard deviation 60For the remaining questions, consider the following problem description: An oil company is considering exploring new well sites S₁, S2, ..., S10 with respective costs C1, C2, C10. And in particular they want to find the least-cost selection of 5 out of the 10 possible sites. The binary decision variables x₁,x2,..., X10 denote the decision to explore the corresponding site.Suppose that Pizza King and Noble Greek stopadvertising but must determine the price they will chargefor each pizza sold. Pizza King believes that Noble Greek’sprice is a random variable D having the following massfunction: P(D $6) .25, P(D $8) .50, P(D $10) .25. If Pizza King charges a price p1 and NobleGreek charges a price p2, Pizza King will sell 10025( p2 p1) pizzas. It costs Pizza King $4 to make a pizza.Pizza King is considering charging $5, $6, $7, $8, or $9 fora pizza. Use each decision criterion of this section todetermine the price that Pizza King should charge.
- minimize Z = 5x1 + x2 subject to 3x1 + 4x2 = 24 0 x1 x1 + 3x2CAN YOU EXPLAIN THREE OUTPUTS OF MARTRIX MODEL CONNNNUNICATION WITH SOME EXAMPLES?Martin owns an older home, which requires minor renovations. However, the neighborhood where Martin lives mostly includes newly constructed luxury homes. Why might Martin's home increase in value? Based on the principle of substitution, the value of Martin's house will equal the value of the newly constructed homes in the neighborhood. ○ The value of Martin's home will decrease due to the new competition in the neighborhood. Based on the principle of regression, the newly constructed homes in the neighborhood will increase the home values of the entire neighborhood. Based on the principle of progression, the newly constructed homes in the neighborhood will increase the home values of the entire neighborhood.
- No probabilities are known for the occurrence of the nature states. Compare the solutions obtained by each of the following criteria: Maximin (Minimax)4 For each of the following, determine the direction in which the objective function increases: a z = 4x, - x2 b z = -x, + 2x2 C z = -x - 3x2Can the function f (x) = - x2 + 3x +2 be maximized?
- Graph the feasible region for the system of inequalities. 4x+y≤3 x-y>3WHAT WLL HAPPEN IF THERE IS A CHANGE IS ONE OF THE OBJECTIVE FUNCTION COEFFICIENT? A. SLOPE OF THE OBJECTIVE FUNCTION LINE ALWAYS WILL CHANGE B. OPTIMAL SOLUTION ALWAYS WILL CHANGE C. ONE OR MORE OF THE DECISION VARIABLES ALWAYS WILL CHANGE D. ALL OF THE ABOVE E. NONE OF THE ABOVEFor minimization linear programming problem, the simplex method is terminated when all values of: a. Z (NB) s0 Ob. None of them Z (NB) = 0 Z (NB) 2 0