Question

In Excel ( solver)

A calculator company produces a scientific calculator and a graphing calculator. Long-term projections indicate an expected demand of at least 100 scientific and 80 graphing calculators each day. Because of limitations on production capacity, no more than 200 scientific and 170 graphing 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 $2 loss, but each graphing calculator produces a $5 profit, how many of each type should be made daily to maximize net profits?

In Excel ( solver)

Answer 1

Let x = scientific calculators
Let y = graphing calculators

Lets make out the constraints

x > 100

y > 80

maximum shipping

x < 200 and y < 170

minimum shipping
x + y > 200

Or

y > –x + 200

Objective function
R = –2x + 5y

100 < x < 200
80 < y < 170
y > –x + 200
Make the graph

now test the corner points

(100, 170)

(200, 170)

(200, 80)

(120, 80)

(100, 100)

Calculate the value of R

R = 650 maximum at (x, y) = (100, 170).

x = scientific calculators = 100
y = graphing calculators = 170