Simultaneous Calculation - Sharp EL-W535TG Operation Manual

Simultaneous Calculation

(This example is for EL-W516T only.)
<Example 1>
To produce one unit of product X, 3 kg of material A and 1 kg of material B
are required.
To product one unit of product Y, 1 kg of material A and 2 kg of material B
are required.
There are 9 kg of A and 8 kg of B in stock.
If the selling price of product X is 300 dollars/unit and the selling price of
product Y is 200 dollars/unit, how many units of product X and how many
units of product Y should be produced in order to maximize sales K?
(Do not include the cost of materials and production or other expenses)
If the quantities produced of each product are x and y, the sales K can be
expressed as
K = 3x + 2y
The following relations hold for the quantities in stock:
3x + y
x + 2y 8
x 0, y 0
Based on these conditions, find the values of x and y that maximize sales K.
9
4
K
2
0
The conditions can be graphed as shown above.
The sales K is a maximum where the line K = 3x + 2y passes through the
intersection point P of lines 3x + y = 9 and x + 2y = 8.
The intersection point P can be obtained from the following simultaneous equations:
3x + y = 9
x + 2y = 8
Solving these gives
x = 2, y = 3
and thus the maximum value of the sales K is
K = 3 x 2 + 2 x 3 = 12 (x 100) dollars (when x = 2 units and y = 3 units)
9
y
K=3x+2y
P
3
x
8
50