Pauline sells computers on commission. She spends 2 hours on
selling a laptop and 1 hour on selling a desktop computer. She works no
more than 40 hours per week and routinely sells at least 1 laptop and at
least 4 desktops each week. To maximize her income, how many of each
type should she sell if her commission is
a. $30 per laptop and $14 per desktop;
b. $30 per laptop and $16 per desktop.
sdada
To maximize Pauline's income, we need to find the combination of laptops and desktops that will yield the highest commission. Let's solve the problem using linear programming.
Let's represent the number of laptops sold as "L" and the number of desktops sold as "D".
Considering the given conditions:
- Pauline spends 2 hours selling a laptop and 1 hour selling a desktop.
- Pauline works no more than 40 hours per week.
- Pauline routinely sells at least 1 laptop and at least 4 desktops each week.
We can create the following inequalities:
1. L ≥ 1 (at least 1 laptop sold)
2. D ≥ 4 (at least 4 desktops sold)
3. 2L + D ≤ 40 (time constraint, they work no more than 40 hours)
Now, let's calculate the commission for each scenario:
a. Commission of $30 per laptop and $14 per desktop:
Commission = 30L + 14D
b. Commission of $30 per laptop and $16 per desktop:
Commission = 30L + 16D
To maximize the commission, we need to solve the following linear programming problem:
Maximize:
a. 30L + 14D
b. 30L + 16D
Subject to:
1. L ≥ 1
2. D ≥ 4
3. 2L + D ≤ 40
Solving this linear programming problem will provide us with the optimal values for L and D, indicating the number of laptops and desktops Pauline should sell to maximize her income.