Question

CarPro is an automobile dealer selling only new cars. CarPro sells three types of vehicles: sedans, SUVs and trucks. CarPro places orders to the car manufacturers only when customers have decided to purchase. The ordering cost (per unit) of sedan, SUV and truck are $18,000, $20,500 and $19,000, respectively. The sales price (per unit) of sedan, SUV and truck are $20,000, $23,000, and $21,500, respectively. The base salary for a sales person is $100/day. In addition, a sales person gets a commission of 5% on the selling price of cars he sells. Each sales person works 8 hours a day. A sales person spends two hours selling a sedan, three hours selling an SUV, and two-and-a-half hours selling a truck. CarPro can spend a maximum of $300,000 per day on ordering cars. How many of each type of car should CarPro sell to maximize profits?

Answer 1

14 truck and 1 suv produce 21,800 profit

Step-by-step explanation:

We have to solve for the contribution margin considering the constraing resourse which, is the ordering cost:

`\left[\begin{array}{cccc}&sedan&SUV&truck&\\$NRV&19000&21850&20425&\\$Cost&-18000&-20500&-19000&\\$CM&1000&1350&1425&\\$Constrain resource&18000&20500&19000&\\$CM per constrain&0.05556&0.0659&0.075&\\\end{array}\right]`

The card models revenue is calcualted using the net realizable value for each card, which is their sales price less the 5% sales commission.

Then we solve for how many truck will it purchase:

300,000 / 19,000 = 15,78

So the company will purchase 15 trucks

giving 15 x 1,425 = 21,375

This will require 2.5 x 15 = 37.5 hours thus 5 sales man (40 labor)

This creates 2.5 hours unsured

and also 300,000 - 15,000 x 19,000 = 15,000 dollar which are not productive

So, we will try to make a better use to purchase the SUV which is the second best option instead of the 15th truck:

giving 14 x 1,425 + 1350 = 21,300

we subtract the 500 dollar of sales man and get a 21,800 profit

with less unproductive dollar. So this will be the answer