Math 1324 Mathematics For Business And Social Sciences

Math 1324 Mathematics For Business Social Sciences Signature Assign

Math 1324: Mathematics for Business & Social Sciences Signature Assignment. “Woody’s Furniture Manufacturing” Woody’s Furniture Manufacturing Company produces tables and chairs. A table requires 8 labor hours for assembling and 2 labor hours for finishing. A chair requires 2 labor hours for assembling and 1 labor hour for finishing. The maximum number of labor hours available per day are 400 hours for assembling and 120 hours for finishing.

1. Let represent the number of tables produced per day by Woody’s Furniture Manufacturing Company, and let represent the number of chairs produced per day. Write a system of four linear inequalities involving and that, when solved, give the set of all ordered pairs of number of tables and number of chairs that Woody’s company can produce per day, given the constraints above. Next to each inequality, write a brief description or interpretation of its meaning. 2. Carefully graph the system of linear inequalities on a separate sheet of graph paper and then shade the feasible region. Is the bounded or unbounded? Identity and label on the graph the coordinates of each of the points. Be sure to attach the graph when you submit your work. 3. For each of the following solutions, determine whether or not it is a feasible solution to the Woody’s Furniture Manufacturing Company problem. Show your work and explain your reasoning. (a) 20 tables per day , 80 chairs per day (b) 50 tables per day , 50 chairs per day (c) 0 tables per day , 0 chairs per day (d) -15 tables per day , -20 chairs per day (e) 5 tables per day , 100 chairs per day (f) 45 tables per day , 30 chairs per day 4. Suppose that each table produced and sold yields a $60 profit and each chair produced and sold yields a $20 profit. (a) An isoprofit line is a line of solution points within the feasible region that each yields that same profit. Find two feasible solutions to the Woody’s Furniture Manufacturing Company problem that produce a total profit of $900, and then find two feasible solutions that produce a total profit of $2,100. Explain your answers, and then draw these two isoprofit lines on your graph- one for total profit of $900, and the other for total profit of $2,100. (b) Finding an optimal solutions: How many tables and chairs should Woody’s company produce each day as to maximize its daily profit? What is Woody’s maximum daily profit? Explain your answers. 1 x y ( ) y x , ( ) y x , x y John Angelo Gotti III is a New York City mobster who during the 1990s led the Gambino crime family of Cosa Nostra for his imprisoned father John J. Gotti. He is also known as the son of the Teflon Don. John Gotti Jr. arrested on murder conspiracy charge. Barcelo for NewsJohn "Junior" Gotti escorted Tuesday morning outside of the Melville, NY, FBI building. John A. (Junior) Gotti was ratted out by a boyhood buddy who gave the feds enough evidence to charge the mob heir Tuesday with three murders - and possibly put him away for life, sources told the Daily News. John Alite, who got his start in crime robbing drug dealers with the Dapper Don's son, was not named as a defendant in the indictment charging Junior with racketeering, murder and cocaine trafficking. Alite, 45, however, was identified by the feds as "a powerful associate of the Gambino crime family" who directed their "criminal enterprise" in Tampa. A career criminal from Ozone Park, Queens, who fled the country in 2004 after he was hit with federal racketeering charges, Alite vowed in an interview two years ago he'd never rat on Gotti. But he also said he feared going to prison. "Either way, I'm a dead man," Alite told the St. Petersburg Times as he sat in a stinking Brazilian jail and fought extradition to Florida for two years. Since then, Alite, who was extradited in December 2006 and could face a murder rap, appears to have decided that crossing Gotti is less dangerous than going to jail, the sources said. Gotti, 44, was arrested by the FBI at his Long Island home at 6 a.m. Tuesday. Though the murders happened in New York, the charges grew out of a decade-long investigation of the Gambino family's operations in Tampa. Displaying none of his late father's sartorial splendor, Junior wore a navy-blue polo shirt and matching sweatpants at his arraignment. "Yes, Your Honor," he politely answered the judge. Manhattan federal prosecutor Elie Honig said at a hearing that the indictment against Gotti "captures a lifetime of criminality," tracing his rise from a street-level enforcer in the 1980s to a cocaine king with a "stable" of dealers in Queens. Honig said Gotti became a "made man" after ordering the December 1988 murder of George Grosso in Queens and "oversaw" the murder of Gambino family soldier Louis DiBono, who was rubbed out on Oct. 4, 1990, in a parking garage of the World Trade Center. John Gotti, the Gambino family boss who died behind bars in 2002, was caught on tape by the feds approving the demise of DiBono because "he refused to come in when I called." Junior was also charged in the Nov. 20, 1991, slaying of Bruce Gotterup in Rockaway Beach, Queens. "Mr. Gotti absolutely denies any involvement with any of the three murders," Gotti attorney Charles Carnesi said. "There is no evidence. ... This is a case based on a drug dealer who wants to avoid going to jail." Carnesi said Gotti was a family man who has stayed out of trouble since his 1999 conviction on racketeering charges. The judge was not swayed by Carnesi's words. He ordered Gotti held without bail and extradited to Tampa for trial. Carnesi said the feds have not set a date to send Gotti to Florida and that he's going to try to have him "plead not guilty by video ... so he can stay up here, at least." Gotti's mother, Victoria, told The News she was "just wiped out." His sister Victoria questioned why Gambino turncoats Salvatore (Sammy Bull) Gravano and Michael (Mikey Scars) DiLeonardo didn't tell the feds "anything about those crimes." "The feds first tried to make John, my brother, a rat - yet he stood trial three times," she told The News. "And now yet again!" The Gambinos aren't the powerful crime family they used to be. The feds gutted the leadership in February when they arrested more than 60 mobsters in New York City and Sicily on charges that include murder, extortion and racketeering. Four other alleged New York wiseguys who had been in cahoots with the Gambinos were named in a related racketeering indictment. Also named was another childhood friend of Junior's, 33-year-old James Cadicamo of Tampa, who is accused of conspiring to kill a Gambino thug who turned government witness. Another of the accused, 47-year-old John Burke of Queens, had been charged as the triggerman in the Gotterup case but was later acquitted. He was doing time for another crime in an upstate prison when he was hit Tuesday with the new racketeering charges. Guy Peden, 47, of Wantagh, L.I., was charged Tuesday with helping Burke kill Gotterup. Burke and David D'Arpino, 33, of Howard Beach, Queens, were also charged with murdering John Gebert in Queens on July 12, 1996. Gotti has not been connected to that crime. The other man indicted on racketeering charges Tuesday was Michael Finnerty, 43, of Oceanside, L.I. Like the others, he faces life in prison if convicted. Gotti was also charged with conspiring to distribute 5 kilos of cocaine, according to the indictment. He remains a suspect in the 1983 stabbing murder of Danny Silva during a brawl at the Silver Fox Bar in Ozone Park, but prosecutors decided the evidence was too weak despite the emergence of a new witness last year, sources said. Links:

Paper For Above instruction

System of Inequalities, Graphing, and Feasible Region

In analyzing the production constraints faced by Woody’s Furniture Manufacturing Company, we define variables that represent the number of tables and chairs produced daily. Let \(x\) denote the number of tables and \(y\) the number of chairs. Based on the given labor hours and resource limitations, we can formulate a system of inequalities.

For the assembly labor hours: Each table requires 8 hours, and each chair requires 2 hours. The total assembly hours cannot exceed 400 hours per day. This constraint can be expressed as:

• \(8x + 2y \leq 400\), which means the combined labor hours for assembling must be less than or equal to the available 400 hours. This inequality ensures that total assembly hours do not surpass the daily maximum.

For the finishing labor hours: Each table takes 2 hours; each chair takes 1 hour. The total finishing hours cannot exceed 120 hours per day. This is represented as:

• \(2x + y \leq 120\), meaning the total finishing hours for all furniture must be within the available 120 hours limit.

Since the production cannot be negative, variables must satisfy the non-negativity constraints:

• \(x \geq 0\) and \(y \geq 0\), indicating that negative production quantities are nonsensical.

These inequalities collectively define the feasible region for the production of tables and chairs, constrained by labor hours and non-negativity. Graphing these inequalities and identifying the feasible region enable decision-making for optimal production within these constraints.

To visualize the feasible region, we would plot the lines corresponding to the equalities \(8x + 2y = 400\) and \(2x + y = 120\), then shade the areas satisfying the inequalities \(8x + 2y \leq 400\) and \(2x + y \leq 120\). The feasible region is the intersection of these shaded regions along with the non-negativity constraints. The region is unbounded because there are no upper bounds on the production quantities apart from the labor hours constraints, which form the boundary lines.

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