Multiple optimal solutions exist when(choose one below) (a) the objective function's level curves are parallel to a constraint (b) for at least one objective function coefficient, the allowable increase/decrease is zero. (c) for at least one constraint, the shadow price is zero. Both (a) and (b). Both (a) and (c). Both (b) and (c). All (a), (b), (c) are true.
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- If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60 per unit. a. How can the monopolist maximize her profit? b. If the monopolist must pay a sales tax of 5% of the selling price per unit, will she increase or decrease production (relative to the situation with no sales tax)? c. Continuing part b, use SolverTable to see how a change in the sales tax affects the optimal solution. Let the sales tax vary from 0% to 8% in increments of 0.5%.what will happen if the right hand side value of a constraint in two variable linear programming problems is changed? a. optimal measure of performance may change b. parallel shift must be made in the graph of that constraint c. optimal valued for one or more of the decision variables may change d. all of the above e. none of the above1. A specific assignment of values to decision variables is called what? a. Constraint b. Feasible c. Solution d. None of the above 2. Which of the following must be true of a feasible solution a. All of what Solver calls changing variables must be greater than 0 b. It is optimal c. It violates no constraints d. None of the above
- 1. If constraint has a shadow price of $6, Right-Hand-Side (RHS) is 12, allowable increase is 2, allowable decrease is 4. How would objective function change if the RHS of this constrains changes from 12 to 9? Answer___________Is my solution correct and did I fully answer the questions? (see attachment for my solution) Question: There are three factories on Momiss River. Each emits two types of pollutants, labeled P1 and P2, into the river. If the waste from each factory is processed, the pollution in the river can be reduced. It costs $1,500 to process a ton of factory 1 waste, and each ton processed reduces the amount of P1 by 0.10 ton and the amount of P2 by 0.45 ton. It costs $2,500 to process a ton of factory 2 waste, and each ton processed reduces the amount of P1 by 0.20 ton and the amount of P2 by 0.25 ton. It costs $3,000 to process a ton of factory 3 waste, and each ton processed reduces the amount of P1 by 0.40 ton and the amount of P2 by 0.50 ton. The state wants to reduce the amount of P1 in the river by at least 125 tons and the amount of P2 by at least 175 tons. a. Use Solver to determine how to minimize the cost of reducing pollution by the desired amounts. Are the LP assumptions…Explain why it is problematic to include a constraint such as the following in an LP model for a blending problem: Total octane in gasoline 1 blend/Barrels of gasoline 1 blend daily ≥ 10
- Select the best statement if we consider the following situation: The right-hand side of a particular constraint is 30. Applying sensitivity analysis to the LP model shows that the shadow price is 1.2 and an allowable increase of 15 and allowable decrease of 10. 1.If 20≤RHS≤45, the change in the objective function value will be 1.2 times the difference between the new value and 30. 2.If 10≤RHS≤15, the change in the objective function value will be 1.2 times the difference between the new value and 30. 3.The objective function value will increase. 4.The objective function value will decrease.Formulate and then solve a linear programming model of this problem, to determine how manycontainers of each product to produce tomorrow to maximize profits. The company makes fourjuice products using orange, grapefruit, and pineapple juice.Product Retail Price per QuartOrange juice $1.00Grapefruit juice .90Pineapple juice .80All-in-One 1.10The All-in-One juice has equal parts of orange, grapefruit, and pineapple juice. Each product isproduced in a one-quart size (there are four quarts in a gallon). On hand are 400 gallons of orangejuice, 300 gallons of grapefruit juice, and 200 gallons of pineapple juice. The cost per gallon is$2.00 for orange juice, $1.60 for grapefruit juice, and $1.40 for pineapple juice.In addition, the manager wants grapefruit juice to be used for no more than 30 percent of thenumber of containers produced. She wants the ratio of the number of containers of orange juice tothe number of containers of pineapple juice to be at least 7 to 5.True or False 1. Given three corner points A, B, and C of a linear programming problem, if A is adjacent to B and B is adjacent to C, then A can be determined from C by interchanging exactly two basic and two nonbasic variables. 2. For a set of primary and dual solutions to be feasible, the objective function value of the primary (Z) can never exceed that of the dual (W) no matter which problem is to maximize and which is to minimize. 3. If the current iteration is degenerate, the next iteration will also be degenerate. 4. The optimal (dual) primary solution can be obtained from the dual (primary) optimal tableau.
- (i) A consumer has income of £3,000. Apple juice is priced at £3 a bottle and cheese is priced at £6 a kilo. Drawthe budget constraint for a consumer with standard preferences. What is the slope of this budget constraint? (ii) Show a consumer’s budget constraint and indifference curves for apple juice and cheese. Show the optimalconsumption choice. If the price of juice is £3 a bottle and the price of cheese is £6 a kilo, what is the marginalrate of substitution at this optimum? (iii) The price of cheese rises from £6 to £10 a kilo, while the price of juice remains at £3 a bottle. For aconsumer with a constant income of £3,000, show what happens to consumption of juice and cheese.Decompose the change into income and substitution effects.How will a change in the right-hand-side value for a constraint affect the optimalsolution?You have been assigned to develop a model that can be used to schedule employees at a local fast-food restaurant. Assume that computer technology has advanced to the point where very large problems canbe solved on a PC at the restaurant.a. What data would you collect as inputs to your model?b. Describe in words several appropriate objective functions for your model.c. Describe in words the constraints needed for your model.