Based on the per-unit increase in the right-hand side of the constraint, the dual price measures the a.decrease in the value of the optimal solution. b.increase in the value of the optimal solution. c.change in the value of the optimal solution. d.improvement in the value of the optimal solution.
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- Dataware is trying to determine whether to give a $10 rebate, cut the price $6, or have no price change on a software product. Currently, 40,000 units of the product are sold each week for $45 apiece. The variable cost of the product is $5. The most likely case appears to be that a $10 rebate will increase sales 30%, and half of all people will claim the rebate. For the price cut, the most likely case is that sales will increase 20%.a. Given all other assumptions, what increase in sales from the rebate would make the rebate and price cut equally desirable?b. Dataware does not really know the increase in sales that will result from a rebate or price cut. However, the company is sure that the rebate will increase sales by between 15% and 40% and that the price cut will increase sales by between 10% and 30%. Perform a sensitivity analysis (two-way data table) that could be used to help determine Dataware’s best decision.The Big Bang Novelty Company (BBNC) makes 3 types of noise?makers: Toot, Wheet, and Honk. A Toot can be made in 30 minutes and has a feather attached to it. A Wheet requires 20 minutes, has two feathers, and is sprinkled with 0.5 ounces of sequin powder. The Honk requires 30 minutes, three feathers, and 1 ounce of sequin powder. The unit profits are $0.45 per Toot, $0.55 per Wheet, and $0.70 per Honk. The following resources are available: 80 hours of labor, 360 feathers, and 90 ounces of sequin powder. BBNC would like to maximize the overall profit from the noise-makers. (a) Write the linear programming model. Express labor time in minutes in LP formulationb) Solve using Excel Solver. How much of the resources (labor, feathers, and sequin powder) will be used by the optimal solution? If the availability of labor increases by 10 hours, what is the optimal total profit? If the unit profit of Wheet is actually only $0.30 instead of $0.55, will this change the solution? How many of each…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 above
- 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%.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…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.
- Which of the following is the converted constraint of 3x + 2y ≥ 35 under maximization of profit in simplex method? a. -3x +2y + S1 = -35 b. 3x +2y + S1 = 35 c. -3x -2y + S1 = -35 d. -3x -2y - S1 = -35 Which of the following is the converted constraint of 3x + 2y ≥ 35 under minimization of profit in simplex method? a. 3x + 2y - S1 + A1 = 35 b. 3x + 2y + S1 + A1 = 35 c. 3x + 2y + S1 - A1 = 35 d. 3x + 2y - S1 - A1 =-35 e. 3x + 2y - S1 + A1 =-35During the first year software will be purchased from a reputable vendor for $3,000,000. An internal team aided by a hired consulting is also used. The payroll for the internal team is $500,000 for the first year and increases by $500,000 in years two and three. Also, $500,000 will be spent on consulting during the first year and $1,000,000 during each of years two and three. $2,000,000 will need to be invested in hardware during the second year and an additional $500,000 investment in hardware will be needed for year three. $200,000 in training will be needed the first year, $500,000 the second year, and $2,000,000 the third year. Management considers the expenditures for the first three years as investment in the system. Management estimates the operating cost of the system to be $2,500,000 (for personnel and other costs) in year 4 and to grow by 6% per year for years 5 through 10. The benefits are estimated to be $4,000,000 for year 4 and to grow by 30% per year for years 5…Spein Company is a diversified company that discloses supplemental financial information on itssegments. The following information is available for 2019:Sales Traceable Costs Allocable CostsSegment X $400,000 $225,000Segment Y 300,000 240,000Segment Z 200,000 135,000Totals $900,000 $600,000 $150,0006Allocable costs are assigned based on the ratio of a segment’s income before allocable costs to totalincome before allocable costs. This is an appropriate method of allocation. Segment Y’s profit for 2019is ____________________.A. 32,400 Small; 8,100 Medium; 1,620 LargeB. 34,808 Small; 8,700 Medium; 1,740 LargeC. 37,010 Small; 9,250 Medium; 1,850 LargeD. 38,505 Small; 9,625 Medium; 1,925 Large
- An advertising firm desires to reach two types of audiences-customers with annual income of more than K40,000 (target audience A) and customers with annual income of less than K40,000 (target audience B). The total advertising budget is K200,000 . One programme of TV advertising costs K50,000while one programme of radio advertising cost K20,000 . Contract conditions ordinarily require that there should be atleast 3 programmes on TV and not more than 5 on radio. Survey indicates that one TV programme reaches 750,000 customers in target audience A and 150,000in target audience B. One radio programme reaches 400,000 customers in target audience A and 260,000 in target audience B. Formulate a linear programming model for this problem Use the simplex method to determine the media mix to maximize the number of customers reached.A goldsmith makes two types of jewelry. A model A ring is made with 1 g of gold and 1.5 g of silver and sells for 25 UM.Another model B ring sells for 30 UM and is made of 1.5 g of gold and 1 g of silver. If you only have 750 gof each metal, how many rings should be made of each type to obtain maximum profit?Requested:- Make Initial Table of the problem.- Obtain the Case Variables- Obtain the Objective Function- Get Restrictions- Create the Simplex Table- Obtain the Optimal Solution and the Slack Variables.Solve this operational research exercise.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.