EXAMPLE:
Miguel has $100 to spend on blue and red pens.
The cost of each blue pen is $6 while a red pen costs $8.
He must buy at least 6 pens of each color, at least 13 pens in total.
(a) Represent the information above in inequalities.
(b) Show the graph of how he can possibly buy the blue and red pens.
(c) If he can sell each blue pen at $8 and each red pen $12, find number of blue and red pens that
he must buy to have the most profit.
Working:
Let x be the number of blue pens and y be the number of red pens that Miguel buys.
If each blue pen is $6, the total cost of x number of blue pens is 6x.
If each red pen is $8, the total cost of y number red pens is 8y.
If Miguel has a maximum of $100 to spend, the total cost of x blue pens and y red pens is
6x + 8y < 100
3x + 4y < 50 (simplest form by dividing 6x + 8y < 100 by 2) à Inequality #1
If Miguel must buy at least 6 pens of each color:
x > 6 à Inequality #2
y > 6 à Inequality #3
If he sells each blue pen at $8, his profit for every blue pen is $2.
His profit for all blue pens à $(2x)
If he sells each red pen at $12, his profit for every red pen is $4.
His profit for all red pens à $(4y)
His total profit is then $(2x + 4y).
Hence, he must buy 6 blue pens and 8 red pens.