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CBSE Class 12-science Answered

A calculator company produces a scientific calculator and a standard calculator. Long-term projections indicate an expected demand of at least 100 scientific and 80 standard calculators each day. Because of limitations on production capacity, no more than 200 scientific and 170 standard calculators can be made daily. To satisfy a shipping contract, a total of at least 200 calculators much be shipped each day. If each scientific calculator sold results in a Rs 2 loss, but each standard calculator produces a Rs 5 profit, how many of each type should be made daily to maximize net profits?
Asked by Topperlearning User | 29 Jul, 2016, 21:56: PM
answered-by-expert Expert Answer

The question asks for the optimal number of calculators, so the variables will stand for that:

x: number of scientific calculators produced
y: number of standard calculators produced

Since they can't produce negative numbers of calculators, the two constraints are x > 0 and y > 0.

But in this case, constraints can be neglected as we have x > 100 and y > 80.

Also from the give data we can conclude that x < 200 and y < 170.

The minimum shipping requirement is x + y > 200.

The revenue relation will be the optimization equation: R = -2x + 5y. So the entire system is:

R = -2x + 5y, subject to: 
100 < x < 200 
80 <  y < 170 
x + y > 200

The feasible region is shaded in the following graph:

 

 

   Corner Points

z = -2x + 5y

A(100, 170)
B(200, 170)
C(200, 80)
D(120,80)
E(100, 100)

z = 650
z = 450
z = 0
z = 160
z = 300


While testing the corner points at A(100, 170), B(200, 170), C(200, 80), D(120, 80), and E(100, 100), the maximum value of R = 650 is obtained at (x, y) = A(100, 170).

That is, the solution is "100 scientific calculators and 170 standard calculators".

Answered by | 29 Jul, 2016, 23:56: PM

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