Max's Mug Shop

            In 2008. Max’s Mug Shop was founded with a simple premise: Sell the best mugs money can buy. Max’s Mug Shop keeps things simple for customers by only selling one type of mug in the store. The design of the mug can be customized, but the size and price of every mug is the same. While some criticize Max’s Mug Shop for lack of options, it’s customers know that a better mug can not be found anywhere else. Max’s Mug Shop’s target market is coffee and tea drinkers who are looking for the best drinking experience.

Part 2

Fixed Costs

Variable Cost

$3 per mug

Price For One Unit

$13

Cost Function

C(q)=6350+3q

Revenue Function

R(q)=13q

Profit Function

P(q)=13q - 6350 +3q

Break Even Point

 13q=6350+3q

10q=6350

635 mugs per month

Interpretation

The break even point represents how many mugs Max's Mug Shop needs to sell per month to "break even" with how much they are spending. Any less than 635 mugs creates a loss and any more creates a profit.

The slope of the cost function represents the additional cost of the creation of each mug, while the slope of the revenue function represents the additional revenue Max's Mug Shop makes for each mug sold.

Profit Function

The break even point is the negative of the regular break even point. It is -6350.

The profit function graph represents the total profit each unit produces.

Part 3

Quantity Produced Each Day

q=85

The marginal cost of producing n=85 units would be $3

The average cost of producing n=85 units would be 6605/30 (for each day in a month) then 220/85 which is $2.58 per unit

1. The marginal revenue of $13 per unit is greater than the average cost of $2.58 per unit, creating profit for Max's Mug Shop

2. 85*30 is 2,550 mugs per month. This is far beyond the break even point of 635 mugs per month.

3. Yes, Max's Mug Shop would still be making money. R(86)-R(85)=13 and C(86)-C(85)=3, so there would still be a profit of $10 the additional unit.

4. The average cost would decrease because the toll of the fixed cost would be spread out more due to the additional units. 

5. Decreasing average costs would help the company. This allows for more profit per unit sold due to a lower cost.

Part 4

 The company should continue to make money over the next five years and continue to be a profitable business. There is a bit of leeway between the average cost per unit and the marginal cost, which allows for fluctuation in sales, both positive and negative. Also, Max's Mug Shop is making a healthy profit on each mug sold.