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 Required17DayMondayTuesdayWednesday1315Thursday19FridaySaturdaySunday141611Incorrect Formulation:X; : the number of employees working on day iMinimize Z- XI + X2 + X3 + X4 + X5 + X6 + X7s.t.X1217X2 2 13X3 2 15X4 2 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, x2, 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:Xị : the number of employees beginning work on day iMinimize Z=x, +x,+x,+x,+x,+x, + X,++x,217+X, + X, + x,2 13+x, +x,2 15+X,2 192 14st.X, + X, +2 16X, +x, +x, + x,+x, 2 11X20, Vi = ,2.7a) Formulate an LP that the production department can use to minimize the total cost instead ofthe number of employees. (Let c: the cost of workers who start work on day i)b) Suppose that the production department can meet its daily requirements using both full-timeand part-time employees (one day at a time). Let p; the cost of a part-time worker on day i.solve part a. 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.DayMondayTuesdayWednesdayThursdayFridaySaturday# of Full-Time Employees Required171315191416Sunday11Incorrect Formulation:X4 : the number of employees working on day iMinimize Z- xi + X2 + X3 + X4 + Xs + Xs + X7s.t. XI2 17X:2 13X3 2 15X42 19Xs 2 14X6 2 16X) 211X 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 correctlyformulating this problem is to realize that the production department's primary decision is not howmany people are working each day but rather bow 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,217+X, + X, + X,2 13**, +x,2 15*X,2 19s.t.X, + X, +X, +X, +x, +X, +x, +X, + x, +X, +X, + X, + x, + x;X, +*, +*, +x, +x,X, +x, + x, +x, + x, 2 11x20, Vi - 2.7214216c) 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 f;(w; – d.).d) Suppose that the production department wants to minimize the maximum of the surpluses oneach day (max (w1 – dı, wz – d2,…..,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.

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.# of Full-Time E

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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 Required17DayMondayTuesdayWednesday1315Thursday19FridaySaturdaySunday141611Incorrect Formulation:X; : the number of employees working on day iMinimize Z- XI + X2 + X3 + X4 + X5 + X6 + X7s.t.X1217X2 2 13X3 2 15X4 2 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, x2, 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:Xị : the number of employees beginning work on day iMinimize Z=x, +x,+x,+x,+x,+x, + X,++x,217+X, + X, + x,2 13+x, +x,2 15+X,2 192 14st.X, + X, +2 16X, +x, +x, + x,+x, 2 11X20, Vi = ,2.7a) Formulate an LP that the production department can use to minimize the total cost instead ofthe number of employees. (Let c: the cost of workers who start work on day i)b) Suppose that the production department can meet its daily requirements using both full-timeand part-time employees (one day at a time). Let p; the cost of a part-time worker on day i.solve part a. 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.DayMondayTuesdayWednesdayThursdayFridaySaturday# of Full-Time Employees Required171315191416Sunday11Incorrect Formulation:X4 : the number of employees working on day iMinimize Z- xi + X2 + X3 + X4 + Xs + Xs + X7s.t. XI2 17X:2 13X3 2 15X42 19Xs 2 14X6 2 16X) 211X 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 correctlyformulating this problem is to realize that the production department's primary decision is not howmany people are working each day but rather bow 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,217+X, + X, + X,2 13**, +x,2 15*X,2 19s.t.X, + X, +X, +X, +x, +X, +x, +X, + x, +X, +X, + X, + x, + x;X, +*, +*, +x, +x,X, +x, + x, +x, + x, 2 11x20, Vi - 2.7214216c) 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 f;(w; – d.).d) Suppose that the production department wants to minimize the maximum of the surpluses oneach day (max (w1 – dı, wz – d2,…..,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.

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