Sunday. Suppose that the production department wants to meet its daily requirements using onlyfull-time employees. Formulate an LP that the production department can use to minimize thenumber of full time employees who must be hired.DayMondayTuesdayWednesdayThursdayFridaySaturdaySunday# of Full-Time Employees Required17131519141611Incorrect Formulation:X, : the number of employees working on day iMinimize Z- xI + x; + X3 + X4 + Xs + X6 + X7s.t.X12 17x: 2 13X3 2 15X42 19Xs 2 14X6 2 16X72 11Xi 20, vi -1,2,.7In this formulation, objective function is not the number of full-time employees. The current objectivefunction counts each employee five times, not once. For example, each employee who starts work onMonday works Monday to Friday and is included in x1, x. x3, X4 and xs. The key to correctlyformulating this problem is to realize that the production department's primary decision is not howmany people are working each day but rather how many people begin work on each day of the week.Correct Formulation:X : the number of employees beginning work on day iMinimize Z= x, + x, +x, +x, + X, + X, + X,+x, +x, +x, +x,217+x, +x, + x,2 13** +x,2 15s.t.X, + X, +X, + X, +x, +X, +X, + x, + x, +X, +*, +X, + x, + X,X, +X, + x, + x, + x,X, + X, + x, + x, + x, 211x 20, Vi - 2.7*x,2 192 142 16c) Suppose that the number of workers needed on day i is d. Let w; be the actual number ofworkers on day i. Formulate an LP where the "cost" of having too many workers on day i is fi(Wi – di).d) Suppose that the production department wants to minimize the maximum of the surpluses oneach day (max (w1 – dị, w? – d3,….., w7 –d;)). Formulate an LP.e) Suppose that the production department wants to ensure that at least 30% of the workers haveSunday off. Formulate a constraint for this case. Sunday. Suppose that the production department wants to meet its daily requirements using onlyfull-time employees. Formulate an LP that the production department can use to minimize thenumber of full time employees who must be hired.# of Full-Time Employees Required17DayMondayTuesdayWednesdayThursdayFridaySaturdaySunday131519141611Incorrect Formulation:X;: the number of employees working on day iMinimize Z=x1 + x2 + X3 + X4 + Xs + X6 + X717 ב s.t.xX2 2 13X3 2 15X4 2 19Xs 2 14X6 2 16X72 11Xị 2 0, vi = 1,2,...,7In this formulation, objective function is not the number of full-time employees. The current objectivefunction counts each employee five times, not once. For example, each employee who starts work onMonday works Monday to Friday and is included in x1, x., x3, X4 and xs. The key to corectlyformulating this problem is to realize that the production department's primary decision is not howmany people are working each day but rather how many people begin work on each day of the week.Correct Formulation:Xị : the number of employees beginning work on day iMinimize Z=x, +x, +x, +x, +X, +x, +X,+*,+x, +*,X, +X, +x, +X, +X, +x, +X +x, +x, +x, +*, + x, + x, + x, + x,x, +x, +x, +X,+x,X, + X, + X, + x, + x, 211x 20, Vi = ,2,.,7+X, +x, + x, +x,217+ x, +x, + x,2 13x+x,2 15*X,2 192 14s.t.2 16

Name: Sunday. Suppose that the production department wants to meet its dail
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Description: Sunday. Suppose that the production department wants to meet its daily requirements using onlyfull-time employees. Formulate an LP that the production department can use to minimize thenumber of full time employees who must be hired.DayMondayTuesday

Question

Sunday. Suppose that the production department wants to meet its daily requirements using onlyfull-time employees. Formulate an LP that the production department can use to minimize thenumber of full time employees who must be hired.DayMondayTuesdayWednesdayThursdayFridaySaturdaySunday# of Full-Time Employees Required17131519141611Incorrect Formulation:X, : the number of employees working on day iMinimize Z- xI + x; + X3 + X4 + Xs + X6 + X7s.t.X12 17x: 2 13X3 2 15X42 19Xs 2 14X6 2 16X72 11Xi 20, vi -1,2,.7In this formulation, objective function is not the number of full-time employees. The current objectivefunction counts each employee five times, not once. For example, each employee who starts work onMonday works Monday to Friday and is included in x1, x. x3, X4 and xs. The key to correctlyformulating this problem is to realize that the production department's primary decision is not howmany people are working each day but rather how many people begin work on each day of the week.Correct Formulation:X : the number of employees beginning work on day iMinimize Z= x, + x, +x, +x, + X, + X, + X,+x, +x, +x, +x,217+x, +x, + x,2 13** +x,2 15s.t.X, + X, +X, + X, +x, +X, +X, + x, + x, +X, +*, +X, + x, + X,X, +X, + x, + x, + x,X, + X, + x, + x, + x, 211x 20, Vi - 2.7*x,2 192 142 16c) Suppose that the number of workers needed on day i is d. Let w; be the actual number ofworkers on day i. Formulate an LP where the &#34;cost&#34; of having too many workers on day i is fi(Wi – di).d) Suppose that the production department wants to minimize the maximum of the surpluses oneach day (max (w1 – dị, w? – d3,….., w7 –d;)). Formulate an LP.e) Suppose that the production department wants to ensure that at least 30% of the workers haveSunday off. Formulate a constraint for this case. Sunday. Suppose that the production department wants to meet its daily requirements using onlyfull-time employees. Formulate an LP that the production department can use to minimize thenumber of full time employees who must be hired.# of Full-Time Employees Required17DayMondayTuesdayWednesdayThursdayFridaySaturdaySunday131519141611Incorrect Formulation:X;: the number of employees working on day iMinimize Z=x1 + x2 + X3 + X4 + Xs + X6 + X717 ב s.t.xX2 2 13X3 2 15X4 2 19Xs 2 14X6 2 16X72 11Xị 2 0, vi = 1,2,...,7In this formulation, objective function is not the number of full-time employees. The current objectivefunction counts each employee five times, not once. For example, each employee who starts work onMonday works Monday to Friday and is included in x1, x., x3, X4 and xs. The key to corectlyformulating this problem is to realize that the production department's primary decision is not howmany people are working each day but rather how many people begin work on each day of the week.Correct Formulation:Xị : the number of employees beginning work on day iMinimize Z=x, +x, +x, +x, +X, +x, +X,+*,+x, +*,X, +X, +x, +X, +X, +x, +X +x, +x, +x, +*, + x, + x, + x, + x,x, +x, +x, +X,+x,X, + X, + X, + x, + x, 211x 20, Vi = ,2,.,7+X, +x, + x, +x,217+ x, +x, + x,2 13x+x,2 15*X,2 192 14s.t.2 16

Accepted Answer

Given

Day
 Number of full-time  Employees Required

Monday
               17

Tuesday…

Day Monday # of Full-Time Employees Required 17 Tuesday Wednesday Thursday Friday Saturday Sunday 13 15 19 14 16 11