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.DayMondayTuesdayWednesday# of Full-Time Employees Required171315ThursdayFridaySaturdaySunday19141611Incorrect Formulation:X, : the number of employees working on day iMinimize Z- xI + x2 + X3 + X4 + Xs + X6 + X7s.t. XI2 17x2 2 13X) 215X42 19Xs 2 14X6 2 16X)211Xi 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:x: : the number of employees beginning work on day ix,+x, +x,*, + x,217+x, + x, + x,2 13*+x,2 15*X,2 19214Minimize Z- x, +x,**x, +X, + X, +s.t.X, + X, + x, + x, +*, +x, *x, +x, + X,X, +x, +x, + X, +X,X, +x, + x, + X, + x, 211x2 0, V i-2.72 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(W; – di).d) Suppose that the production department wants to minimize the maximum of the surpluses oneach day (max (w1 – dı, w2 – dz.., 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.DayMondayTuesday

Given :Min Z=x1+x2+x3+x4+x5+x6+x7S.t.…

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Sunday. Suppose that the production department wants to meet its daily requirements using o full-time employees. Formulate an LP that the production department can use to minimize number of full time employees who must be hired. Day Monday Tuesday Wednesday Thursday # of Full-Time Employees Required 17 13 15 19 Friday Saturday 14 16 Sunday 11 Incorract Formulation

Sunday. Suppose that the production department wants to meet its daily requirements using o full-time employees. Formulate an LP that the production department can use to minimize number of full time employees who must be hired. Day Monday Tuesday Wednesday Thursday # of Full-Time Employees Required 17 13 15 19 Friday Saturday 14 16 Sunday 11 Incorract Formulation

MATLAB: An Introduction with Applications

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Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Concept explainers

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.

Topic Video

Question

Sunday. Suppose that the production department wants to meet its daily requirements using only
full-time employees. Formulate an LP that the production department can use to minimize the
number of full time employees who must be hired.
Day
Monday
Tuesday
Wednesday
# of Full-Time Employees Required
17
13
15
Thursday
Friday
Saturday
Sunday
19
14
16
11
Incorrect Formulation:
X, : the number of employees working on day i
Minimize Z- xI + x2 + X3 + X4 + Xs + X6 + X7
s.t. XI2 17
x2 2 13
X) 215
X42 19
Xs 2 14
X6 2 16
X)211
Xi 20, vi - 1,2..7
In this formulation, objective function is not the number of full-time employees. The current objective
function counts each employee five times, not once. For example, each employee who starts work on
Monday works Monday to Friday and is included in x1, x2. X3, x4 and xs. The key to correctly
formulating this problem is to realize that the production department's primary decision is not how
many 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 i
x,+x, +x,
*, + x,217
+x, + x, + x,2 13
*+x,2 15
*X,2 19
214
Minimize Z- x, +x,**
x, +
X, + X, +
s.t.
X, + X, + x, + x, +
*, +x, *x, +x, + X,
X, +x, +x, + X, +X,
X, +x, + x, + X, + x, 211
x2 0, V i-2.7
2 16
c) Suppose that the number of workers needed on day i is d.. Let w, be the actual number of
workers on day i. Formulate an LP where the “cost" of having too many workers on day i is fi
(W; – di).
d) Suppose that the production department wants to minimize the maximum of the surpluses on
each day (max (w1 – dı, w2 – dz.., w7 –d;)). Formulate an LP.
e) Suppose that the production department wants to ensure that at least 30% of the workers have
Sunday off. Formulate a constraint for this case.

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