1.
Tots Toys makes a plastic tricycle that is composed of three
major components: a handlebar-front wheel-pedal assembly, a
seat and frame unit, and rear wheels. The company has orders for
12,000 of these tricycles. Current schedules yield the following
information.
Componen
t
Front
Seat/Fram
e
Rear
wheel
(each)
Available
Requirement
s
Plastic
Cost to
Time
3
4
10
6
.5
2
.1
50000
16000
0
3000
0
Space Manufactur
e
2
8
2
6
1
Cost to
Purchas
e
12
9
3
The company obviously does not have the resources available to
manufacture everything needed for the completion of 12000
tricycles so has gathered purchase information for each
component. Develop a linear programming model to tell the
company how many of each component should be manufactured
and how many should be purchased in order to provide 12000
fully completed tricycles at the minimum cost.
ANS:
Let
FM = number of fronts made
SM = number of seats made
WM = number of wheels made
FP = number of fronts purchased
SP = number of seats purchased
WP = number of wheels purchased
Min
8FM + 6SM + 1WM + 12FP + 9SP + 3WP
s.t.
2. Larkin Industries manufactures several lines of decorative and
functional metal items. The most recent order has been for 1200
door lock units for an apartment complex developer. The sales and
production departments must work together to determine delivery
schedules. Each lock unit consists of three components: the knob
and face plate, the actual lock itself, and a set of two keys.
Although the processes used in the manufacture of the three
components vary, there are three areas where the production
manager is concerned about the availability of resources. These
three areas, their usage by the three components, and their
availability are detailed in the table.
Lock
Key
(each)
Available
Brass Alloy 12
5
1
15000 units
Machining
18
20
10
36000 minutes
Finishing
15
5
1
12000 minutes
Resource
Knob and Plate
A quick look at the amounts available confirms that Larkin does
not have the resources to fill this contract. A subcontractor, who
can make an unlimited number of each of the three components,
quotes the prices below.
Component
Subcontractor
Cost
Larkin Cost
Knob and Plate
10.00
6.00
Lock
9.00
4.00
Keys (set of 2)
1.00
.50
Develop a linear programming model that would tell Larkin how to
fill the order for 1200 lock sets at the minimum cost.
Let X1, X2 and X3 be the number of knob & faceplate , lock and
keys produced by Larkin Industries. The remaining numbers
(1200 –X1) of Knob & Plate, (1200-X2) of Lock and (1200-X3) of
keys are to be ordered from the subcontractor. The additional cost
for these items are (10.00-6.00) = 4 , (9.00-4.00) = 5.00 and
(1.00-0.50) =0.500 respectively.
Thus the objective function can be written as
Minimize Z = 4*(1200-X1) +5*(1200-X2) + 0.5*(1200-X3)
Subject to
12X1 + 5X2 + X3 ≤ 15000
Constraint for Brass Alloy
18X1 + 20X2 + 10X3 ≤ 36000
Constraint for Machining
15X1 + 5X2 + X3 ≤12000
Constraint for Finishing
X1 ≥0 , X2 ≥0, X3 ≥0
Solving this LPP we can find out the optimum number of Knob &
Plate Lock and Key
1.
The number of cans of soft drinks sold in a machineeach week is
recorded below. Develop forecasts usinga three period moving
average.338, 219, 278, 265, 314, 323, 299, 259, 287, 302
Let X
t
denote the number of cans of soft drinks sold in a machine of the t
th
week.Now the 3 month moving average of the t+1th week is given by
Xt + Xt-1 + Xt-2
Ft=3
, t=3, 4, & 5
4.
The number of pizzas ordered on Friday evenings between
5:30 and 6:30 at a pizza delivery location for the last 10 weeks is shown
below. Use exponential smoothing with smoothing constants of .2 and .8
to forecast a value for week 11. Compare your forecasts using MSE.
Which smoothing constant would you prefer?
58, 46, 55, 39, 42, 63, 54, 55, 61, 52
6. A trend line for the attendance at a restaurant'sSunday brunch is given
by Number = 264 + .72(t)How many guests would you expect in week
20?
We have to put the value 20 in the place of‘t’ and we get,Number=264+
(0.72*20) we get
Number= 278.4 nos. Or 278 nos.
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