Question

(i) They have to sell at least 3 graphite rackets. (ii) They have to sell at least 5 titanium rackets. (iii) The combined number of graphite and titanium rackets sold is at most 18 total. If the store's profit is $140 per graphite racket sold and $160 per titanium racket sold, Then how many of each type of racket should the store sell in order to maximize their profit, and how much will their profit be?

Answer 1

1. Assign some variables: say [graphite rackets] = g and [titanium rackets] = t
2. Create equations/inequalities:
\[g+t\ge 18\]
140g + 160t = profit

Answer 2

They have to sell at least 3 g's and 5 t's. So that causes the remaining g + t sum to be >= 10.
If you want to maximize the profit, you would sell the rest of the products at the highest price possible, right? So of the 10 potential remaining products, you would have them ALL be t's, just to get more money.

Answer 3

Summary:
g = 3 (required)
t = 5 (required) + 10 (remaining) = 15

The easy part, I'd say, is finding the profit. Just plug these numbers in the expression 140g+160t

Answer 4

Thanks mate.

Answer 5

my pleasure