Luca’s  Gelato Factory & Store  produces and sells various flavors of ice-cream buckets. There are flavors like coffee, raspberry, passion fruit and regular. The main target audience are retails such as restaurant owners, small ice cream shops, school cafeterias, individuals and etc. The company has been functioning since 1992 and has a strong outlook of growth in the future. It is family founded and operated. All the ingredients used are organic and locally sourced. 

• The start up costs for opening the factory and stores were as such:
• Rent per month $2,500
• Equipment and machinery $1,500
• Supplies $1,000
• Utilities $1,500

• The variable costs of labor and raw materials to produce units is $15
• One bucket of ice-cream sells for $43  
• Cost function 

C(q) = fixed costs () + (variable costs () * quantity ()

C(q) = 8,500 + 15q

• Revenue function

R(q) = price () * quantity ()

R(q) = 43q

• Profit function

P(q) = R(q) - C(q)

P(q) = (43q) - (8,500 + 15q)  

• Break-even Point

Total Revenue = Total Cost

43q= 8,500 + 15q

q=303.57

The break even point is when total cost equals total revenue. In other words, it is when Luca’s Gelato Factory & Store’s does not make any profit nor any gains from the sale and manufacturing of the icecream. At approximately 304 buckets of gelato sales, his company covers the cost of manufacturing and does not make any loss or profit.Anywhere above the point is be marked as a profit for the company and anywhere bellow as a loss

The marginal cost for the factory is $15 for each additional bucket that the factory manufactures. It is the variable cost for each additional unit.

Marginal revenue is the revenue of  $43 per each additional sale of ice cream bucket that the factory sells.   

On the profit function, the break-even point is where the line touches the x-axis. Making the value on the y-axis zero (303.57, 0). As sales of gelato buckets increase, the profit function increases accordingly. At 303.57 (rounding up to 304), the company is not making any profits or losses.  At anywhere above the red dot (break-even point), the company will be making a profit and anywhere bellow it will be making a loss.

Part Three

There are  Q=25 buckets that are produced on a daily basis. 

• Since the cost of producing one unit is $15, the marginal cost for producing 25 buckets of gelato MC = 15*25

MC =  375

It costs $375 to produce 25 buckets daily

• The average cost = (15*25+ 8,500)/25= 355

The average cost for producing 25 units per day is $355 

1. Marginal Revenue is greater that the marginal cost. Marginal revenue q=375  and marginal cost is q=355
2. The number of units sold daily 25 is below the break-even point. That means that until the break-even point being 304, there are 279 units left to sell. In order to sell the remaining 279 buckets of gelato we need approximately 11 days.  (279/25)=11.16
3. If the company increases it’s production by 1 unit it will still make money. While the marginal cost will stay the same, the average cost will decrease. The additional unit will bring in more revenue. Instead of R(q) = 43q, it will be R(q) = (43+1)q. The total cost will also increase but that just means that the company will reach the break-even point faster. C(q+1)- C(q)

R(q) = 43(1000)= 43,000

R(q) = 43(1001)=43,043

R(q + 1) – R(q)= 43

C(q) = 8,500 + 15(1000) = 23500

C(q) = 8,500 + 15(1001)=23515

R(q)-C(q)

43,000-23,500=19,500

R(q+1)-C(q+1)

43,043-23,515=19,528

19,528-19,500=28

Overall, it is beneficial for the company to produce the extra gelato bucket by a margin of $28

4. At q=n, the increase of production decrease average cost. Since we are dividing the fixed cost by a larger quantity, the average cost will proportionally get smaller. 

5. Decreasing the average cost is better for the company because Luca’s gelato factory will be able to produce the gelato at a lower cost and increase the income.

Part FOUR

1. Based on the information provided, the company has a strong future. It makes large sales and therefore very quickly in the month covers it’s manufacturing costs and gaining large profits.
2. In the next 5 years the company will thrive because we as a population become more aware of the benefits of healthy-organic  ingredients and earth conscious decisions. Having natural ice cream is more valued than the one with preservatives. We also become more conscious about where the ingredients are coming from, going to the  down the food chain we can see pasture fed and no chemically treated cows, range free chicken eggs and so on. Making the gelato a prime go to for a treat.