Chapter
7 Practice Questions
7.105
As a supervisor of a production department, you must decide the daily
production totals of a certain product that has two models, the deluxe and the
special. The profit on the deluxe model is $12 per unit and the
special's profit is $10. Each model
goes through two phases in the production process, and there are only 100
man-hours available daily at the construction stage and only 80 man-hours
available at the finishing and inspection stage.
Each deluxe model requires 20 minutes of construction time and 10 minutes
of finishing and inspection time. Each
special model requires 15 minutes of construction time and 15 minutes of
finishing and inspection time. The
company has also decided that the special model must comprise at least 40
percent of the production total.
(a) Formulate this as a linear programming problem.
(b) Find the solution that gives the maximum profit.
7.106
The Fido Dog Food Company wishes to introduce a new brand of dog biscuits
(composed of chicken and liver flavored biscuits) that meets certain nutritional
requirements. The liver flavored
biscuits contain 1 unit of nutrient A and 2 units of nutrient B, while the
chicken flavored ones contain 1 unit of nutrient A and 4 units of nutrient B.
According to federal requirements, there must be at least 40 units of
nutrient A and 60 units of nutrient B in a package of the new mix.
In addition, the company has decided that there can be no more than 15
liver flavored biscuits in a package. If
it costs 1 cent to make a liver flavored biscuit and 2 cents to make a chicken
flavored one, what is the optimal product mix for a package of the biscuits in
order to minimize the firm's cost?
(a) Formulate this as a linear programming problem.
(b) Solve this problem graphically, giving the optimal values
of all variables.
(c) Are any constraints redundant?
If so, which one or ones?
(d) What is the total cost of a package of dog biscuits using
the optimal mix?
7.110
Solve the following linear programming problem using the corner point
method.
Maximize 3 X + 5Y
Subject to: 4X + 4Y £
48
1X + 2Y £
20
Y ³ 2
X, Y ³ 0
7.119
Two advertising media are being considered for promotion of a product.
Radio ads cost $400 each, while newspaper ads cost $600 each.
The total budget is $7,200 per week.
The total number of ads should be at least 15, with at least 2 of each
type, and there should be no more than 19 ads in total.
The company does not want the number of newspaper ads to exceed the
number of radio ads by more than 25 percent.
Each newspaper ad reaches 6,000 people, 50 percent of whom will respond;
while each radio ad reaches 2,000 people, 20 percent of whom will respond.
The company wishes to reach as many respondents as possible while meeting
all the constraints stated. Develop
the appropriate LP model for determining the number of ads of each type that
should be placed?
Chapter 6 Practice Questions
6.110
Furniture Manufacturers Inc., uses 20,000 loads of lumber per year.
A load of lumber costs $500 and the carrying cost is 10 percent of the
unit cost. The cost to
order is $200 per order and the lead time is three working days.
Determine (assume 200 working days):
(a)
the economic order quantity
(b)
the reorder point
(c)
number of orders per year
(d)
days between orders
6.112
We use 1,200 of a certain spare part that costs $25 for each order and
has a $24 annual holding cost. Calculate
the total cost for order sizes of: 25, 40, 50, 60, and 100.
Identify the economic order quantity and consider the implications for
making an error in calculating the economic order quantity.
6.114
David and Beth Sheba run a health food store.
Their top selling item is called Heavenly Kelp.
The annual demand for this is 810 units, and demand is constant
throughout the year. The cost of
placing an order is $20, while the holding cost per unit per year is $4.
(a)
How many orders per year should be placed if they wish to minimize their
total cost?
(b)
What is the minimum possible annual holding cost?
6.116
Purinnerds Dog Food is a very popular product at Kay Gnein's corner
grocery. Demand for this is
relatively constant, and the total demand for the year is 1,200 bags.
The cost of placing an order is $50, while the holding cost is $3 per
unit per year. The store is open
300 days per year. Lead time for
this is 8 days.
Used
for practice Test - for test, change numbers
(a) If
Kay places 50 orders per year, what would her ordering and holding costs be?
(b) If
Kay wishes to minimize her total inventory cost, how many units should she order
each time an order is placed?
(c) What
is the reorder point?
(a)
Let X1 = number of deluxe models produced
X2
= number of special models produced
Maximize
12X1 +
10X2
Subject
to: 1/3X1 + 1/4X2 £
100
1/6X1
+ 1/4X2 £
80
-0.4X1
+ 0.6X2 ³
0
X1, X2 ³
0
(b)
Optimal solution: X1 =
120, X2 = 240
Profit = $3,840
7.106
ANSWER:
(a)
Let X1 = number of liver flavored biscuits in a package
X2
= number of chicken flavored biscuits in a package
Minimize
X1 + 2X2
Subject
to: X1 + X2 ³
40
2X1
+ 4X2 ³
60
X1
£
15
X1,
X2 ³
0
(b)
Corner points (0,40) and (15,25)
Optimal
solution is (15,25) with cost of 65.
(c)
2X1 + 4X2 ³
60 is redundant
(d)
minimum cost = 65 cents
7.110
ANSWER:
Feasible
corner points (X,Y): (0,2) (0,10)
(4,8) (10,2)
Maximum
profit is 52 at (4,8).
7.119
ANSWER:
Let
R = number of radio ads placed
N
= number of newspaper ads placed
Maximize:
0.20*2000R + 0.50*6000N
or
Maximize:
500R + 3000N
Subject
to: R + N ³
15
R
+ N £
19
400R
+ 600N £
7200
1.25R
- N ³ 0
R
³
2
N
³
2
R,
N ³
0
6.110
ANSWER:
(a)
EOQ = 400 units, (b) ROP = 100(3) = 300 units, (c) number of orders per year =
D/Q = 2000/400 = 50 orders
(d)
days between orders = 200/50 = 4 days
6.112
ANSWER:
Total
Cost = total ordering cost + total holding cost
Q
= 25
TC = 1200 + 300 = $1,500
Q
= 40
TC = 750 + 480 = $1,230
Q
= 50
TC = 600 + 600 = $1,200
Q
= 60
TC = 500 + 720 = $1,220
Q
= 100 TC = 300 +
1200 = $1,500
Small variations in order quantity will not have a significant impact on total costs.
6.114
ANSWER:
(a)
EOQ = 90 units. Therefore, the
number of orders per year is 810/90 = 9 orders per year.
(b)
(90/2)4 = $180 total holding cost
6.116
ANSWER:
(a)
With 50 orders per year, Q=24. TC
= TOC + THC = 2500 + 36 = $2,536
(b)
EOQ = 200
(c)
ROP = (1200/300)8 = 32 units
End