Suppose you are a design engineer for a company that manufactures consumer electronic devices and you are estimating the cost of producing a new product. The product has four components that are purchased from electronic parts suppliers and assembled in your factory. You have received cost information from your suppliers for each of the parts; as is typical in the electronics industry, the cost of a part depends on the number of parts you order from the supplier.
Your assembly cost for each unit include the cost of labor and your assembly plant. You have estimated that these costs are C0=$45.00/unit.
The cost of each part depends on the number of parts purchased; we will use the variable n to represent the number of parts, and the variables CA, CB, CC, and CD to represent the unit cost of each type of part. These cost are given in the following tables.
n |
CA |
|---|---|
| 1-4 | $16.00 |
| 5-24 | $14.00 |
| 25-99 | $12.70 |
| 100 or more | $11.00 |
n |
CB |
|---|---|
| 1-9 | $24.64 |
| 10-49 | $24.32 |
| 50-99 | $24.07 |
| 100 or more | $23.33 |
n |
CC |
|---|---|
| 1-24 | $17.98 |
| 25-49 | $16.78 |
| 50 or more | $15.78 |
n |
CD |
|---|---|
| 1-9 | $12.50 |
| 10-99 | $10.42 |
| 100 or more | $9.62 |
Cunit = C0 + CA + CB + CC + CD. To find the unit cost to build one unit, we look in the above tables with a value of n=1; the unit cost is
$45.00+$16.00+$24.64+$17.98+$12.50 = $116.12To find the unit cost to build 20 units, we look in the above tables with a value of
n=20 and get
$45.00+$14.00+$24.32+$17.98+$10.42 = $109.72As expected, the unit cost for 20 units is lower than the unit cost for one unit.
Exercise 1
Create an if statement that will assign the proper cost to the variable CA based on the value of the variable n.
Solution
if n >= 1 && n <= 4
CA = 16.00;
elseif n >= 5 && n <= 24
CA = 14.00;
elseif n >= 25 && n <= 99
CA = 12.70;
else
CA = 11.00;
end
Exercise 2
Create a script that will compute the total unit cost Cunit for a given value of the variable n.
Solution
This code by BrieAnne Davis:
if n>=1 && n<=4; %if n=1 to 4, CA is $16.00
CA=16.00;
elseif n>=5 && n<=24; %if n=5 to 24, CA is $14.00
CA=14.00;
elseif n>=25 && n<=99; %if n=25 to 99, CA is $12.70
CA=12.70;
elseif n>=100; %if n=100 or more, CA is $11.00
CA=11.00;
end %this ends the if statement for CA
if n>=1 && n<=9; %if n=1 to 9, CB is $24.64
CB=24.64;
elseif n>=10 && n<=49; %if n=10 to 49, CB is $24.32
CB=24.32;
elseif n>=50 && n<=99; %if n=50 to 99, CB is $24.07
CB=24.07;
elseif n>=100; %if n=100 or more, CB is $23.33
CB=23.33;
end %this ends the if statement for CB
if n>=1 && n<=24; %if n=1 to 24, CC is $17.98
CC=17.98;
elseif n>=25 && n<=49; %if n=25 to 49, CC is $16.78
CC=16.78;
elseif n>=50; %if n=50 or more, CC is $15.78
CC=15.78;
end %this ends the if statement for CC
if n>=1 && n<=9; %if n=1 to 9, CD is $12.50
CD=12.50;
elseif n>=10 && n<=99; %if n=10 to 99, CD is $10.42
CD=10.42;
elseif n>=100; %if n=100 or more, CD is $9.62
CD=9.62;
end %this ends the if statement
CO=45.00;
Cunit=CO + CA + CB + CC + CD;
Exercise 3
Create a m-file script that will compute and plot the total unit cost as a function of n for values of n from 1 to 150.
Solution
This code was originally written by Bryson Hinton and then modified:
cunit = zeros(1,150);
c0 = 45;
for n=1:150
%compute price for part A
if n >= 1 && n <= 4
ca=16;
elseif n >= 5 && n <= 24
ca=14;
elseif n >= 25 && n <= 99
ca=12.7;
else
ca=11;
end
%compute price for part B
if n >= 1 && n <= 9
cb=24.64;
elseif n >= 10 && n <= 49
cb=24.32;
elseif n >= 50 && n <= 99
cb=24.07;
else
cb=23.33;
end
%compute price for part C
if n >= 1 && n <= 24
cc=17.98;
elseif n >= 25 && n <= 49
cc=16.78;
else
cc=15.78;
end
%compute price for part D
if n >= 1 && n <= 9
cd=12.50;
elseif n >= 10 && n <= 99
cd=10.42;
else
cd=9.62;
end
%sum cost for all parts
cunit(n)= c0+ca+cb+cc+cd;
end
% Plot cost as a function of n
plot(1:150,cunit);
xlabel('n (units)');
ylabel('cost (dollars)');
title('Cost/unit as a function of number of units');
|
Exercise 4
Suppose that you decide to fire your workers, close down your plant, and have the assembly done offshore; in this arrangement, C0 = Cx + Cs, where Cx is the cost of offshore assembly and Cs is the cost of shipping assembled units from the assembler to your warehouse. After some investigation, you find an offshore assembler that gives you the following assembly costs as a function of the number of units to assemble:
n |
Cx |
|---|---|
| 1-29 | $40.00 |
| 30-59 | $30.00 |
| 60 or more | $22.00 |
n |
Cs |
|---|---|
| 1-9 | $20.00 |
| 10-24 | $18.00 |
| 25-74 | $16.00 |
| 75 or more | $15.00 |
