Delivery Driver's Weekly Net-Pay Target
Denise drives for a regional delivery app. She is paid $3.50 per delivery plus $0.62 per mile driven. Her car costs her about $0.21 per mile in fuel and maintenance. This week she has already completed 140 deliveries and driven 410 miles. Her goal is net earnings of at least $1,050 for the week. For the rest of the week she expects each additional delivery to require an average of 2.5 miles of driving. She can accept at most 60 more deliveries before her car needs scheduled service. Denise wants to know whether her goal is reachable and what pay change would make the biggest difference.
1. Write and solve an inequality to find the minimum number of additional deliveries Denise needs to reach her $1,050 net-earnings goal. Interpret the result in context.
Read the worked answer
Net pay per additional delivery is the delivery fee plus mileage pay minus mileage cost:
$3.50 + (0.62 - 0.21)(2.5) = 3.50 + 0.41(2.5) = 3.50 + 1.025 = 4.525$ dollars per delivery.
Current net earnings are:
$140(3.50) + 410(0.62 - 0.21) = 490 + 410(0.41) = 490 + 168.10 = 658.10$ dollars.
Let $d$ be additional deliveries. The inequality is
$658.10 + 4.525d \ge 1050$.
Then $4.525d \ge 391.90$, so $d \ge 86.61$. Since deliveries are whole, she needs 87 more deliveries. Check: 86 gives $658.10 + 389.15 = 1047.25$, which is short; 87 gives $1051.78$, which meets the goal.
2. Denise's service cap is 60 more deliveries. Does the cap prevent her from reaching the goal? If so, what minimum per-mile pay rate would let 60 more deliveries meet the goal, holding all other figures fixed?
Read the worked answer
At the current rate, 60 more deliveries add $60(4.525) = 271.50$, for a total of $658.10 + 271.50 = 929.60$, which is below $1,050. The cap does prevent her from reaching the goal.
Let $r$ be the per-mile pay rate. Net pay per delivery becomes $3.50 + (r - 0.21)(2.5) = 2.975 + 2.5r$. With 60 deliveries:
$658.10 + 60(2.975 + 2.5r) \ge 1050$
$658.10 + 178.50 + 150r \ge 1050$
$150r \ge 213.40$
$r \ge 1.4227$.
She would need a mileage rate of about $1.43 per mile, holding the per-delivery fee and costs fixed.
3. Denise can negotiate either a $0.50 increase in the per-delivery fee or a $0.10 increase in the per-mile rate. With the 60-delivery cap, which option gets her closer to the $1,050 goal? Support with calculations.
Read the worked answer
Option A, +$0.50 per delivery: net per delivery becomes $4.525 + 0.50 = 5.025$. With 60 deliveries, total net is $658.10 + 60(5.025) = 658.10 + 301.50 = 959.60$.
Option B, +$0.10 per mile: each delivery has 2.5 miles, so net per delivery rises by $0.10(2.5) = 0.25$, to $4.775$. Total net is $658.10 + 60(4.775) = 658.10 + 286.50 = 944.60$.
Option A gives $959.60, which is $15.00 higher than Option B. Neither reaches $1,050 within the 60-delivery cap, but the per-delivery increase is the better choice.