Management at Gordon Electronics is considering adopting a bonus system to increase production. One suggestion is to pay a bonus on the highest 5% of production based on past experience. Past records indicate weekly production follows the normal distribution. The mean of this distribution is 4,000 units per week and the standard deviation is 60 units per week. If the bonus is paid on the upper 5% of production, the bonus will be paid on how many units or more?

4,099 units or more

Explanation:

The cumulative distribution of a random variable X that follows a normal distribution is given by the area undear the "bell curve" and the values are given by the corresponding table for the standard normal distribution.

The standardized value of the variable X is called Z and is calculated with the formula:

         

Where:

         

         

You read the Z-value for which the probability is greater than or equal to 5% in the table for the values of the area to the right of Z. Using probability = area under the curve ≥ 5%, the Z-value is 1.645 (interpolating between p = 0.0495, Z = 1.64 and p = 0.0505, Z = 1.65).

Substituting in the formula for Z:

1.645 = (X - 4,000) / 60X= 60 × 1.645 + 4,000 = 4,098.7 ≈ 4,099

Hence, the bonus will be paid on 4,099 units or more.

You are planning a coffee company, This would depend on an amount of customers, location of the company, and how you are going to distribute the product. It will also depend on the source of your products, and the economic and political standpoint of each individual country

1) The buying price should encompass many "thoughts":

It must be small enough to give you a profitThe price of the product must not meet or exceed your selling price, for to continue to do business with them, you must be able to earn a profit.It must be large enough so that both the buyer and seller is happyTo keep both the buyer and seller happy, the buyer must be able to give a reasonable price that would ensure a continuation of the product, which means buying in a price that would allow the seller to pay for employees, cover businesses expenditures, etc.

This may place the price in a higher amount, so you must ensure that your product is high-quality to offset the price. For in the balance of price vs customer, the higher the price, the less customers (unless you are a monopoly (which you are not), or you have loyalty.)

2) To calculate the possible earnings, you must subtract the costs from the total revenue you have gotten (to find the profit).

The costs can include: shipment, supplies, electricity, upkeep of store(s), taxes (property, business, etc), royalty to coffee-company, ad-costs (if you decide to run them), etc.

For example, let us say that:

Total cost for:

Shipment: $300 per shipment (10 shipments = 10 x 300 = $3000)Royalty: $1000Tax: $300Payment to sources: $0.10 a lb.Cost for 500 lbs. of coffee

500 x 0.10 = 50

3000 + 1000 + 300 + 50 = $4,350

This means that total cost for shipment of resources needed is $4,350.

Now, let us calculate the cost of the business itself:

For example:

Total cost for:

Building maintenance: $5,000

Pay for employees as a whole for 30 days: $6,000

Electricity, Gas, and other power source: $2,000

Total cost: 5000 + 6000 + 2000 = $13,000

Total cost for extra workers (repairs): $3,000

Tax as a whole: $16,000

16000 + 3000 = 19,000

This means that total cost is:

$13,000 + $19,000 + 4,350= $36350

So we must calculate the amount needed to break even and make a profit.

Let us say that you want to make a $10000 profit.

Add $36350 with $10000, which equals $46,350

=>

After a month, you find that approximately 50,000 customers show up (returns are counted too) in total to your stores because they find that your products are good

Divide $46,350 with 50,000

46,350/50,000 = ~0.93

However, 93¢ is a weird number to sell coffee, and so we will round up to $1.00

This means that you sell each cup of coffee at $1.00

3) The cost of production is $36,350, with the total revenue being a projected amount of $46,350 - $50,000

Subtract the range with the production

$46,350 - $36,350 = 10,000

$50,000 - $36,350 = 13650

The total profit is projected to be from $10,000 - 13,650

=> Remember revenue & profit is usually poured back into the company, and so the amount is subject to change in a year to year process. Also, the percentage of loyalty & new customers may change as well. Political events around the world may affect sales. Overseas openings of shops may also have an effect on the company.

~Rise Above the Ordinary