Answer:

Appalachia Beverage Company Inc. has two alternatives:

Alternative 1 : Construct a single plant with capacity of 300,000 cases, a monthly fixed cost of $262,500 and a variable cost of $3.25 per case.

Alternative 2 : Construct 3 plants with capacities of 120,000; 100,000 and 80,000 with monthly fixed cost of $120,000, $110,000 and $95,000 and variable cost $3 per case.

(A)Breakeven level of output is the quantity of output where the total revenue equals total cost. The break-even quantity can be calculated using the formula:

Alternative 1:

Where Q=Quantity, VC=variable cost, FC=fixed cost, TR=total revenue, TC=Total cost, price.

The breakeven quantity where total revenue is equal to total cost is 150000 cases.

Alternative 2:

The breakeven quantity where total revenue is equal to total cost is 162500 cases.

(B)At wholesale price of $5 and sales at 200,000 , the profits under two alternatives are:

Similarly the profit for alternative 2 is:

The profit for alternative one and two are $87500 and $75000 respectively. Option 1 gives greater profits than the second one.

(C)If sales increase to production capacity of 300,000, then profit for both alternatives would be:

Similarly the profit for alternative 2 is:

The profit for alternative one and two are $262500 and $275000 respectively and hence multiple plant, option 2, should be chosen.

Answer:

The power brokers Inc. has a fixed cost $4,500 per month and average variable cost of ($59 - 0.006Q). The commission on stock is $100 per trade with 35% to sales representative, which mean $65 per trade.

(A)The quantity at which a profit of $7500 is generated can be calculated by equating the difference in total revenue and total cost to profit as below:

By putting profit=$7500, the quantity can be calculated:

On solving the above equation:

As the quantity cannot be in negative, the answer is 1,000.

(B)The point cost elasticity is the relation between cost and output. The point cost elasticity is defined as:

Where C=total cost, MC=marginal cost, Q=Quantity

It is given that AVC

Therefore cost elasticity at Q=1000 is:

This explains that if the output increases by 1%, there is 0.817% increase in cost. This is a situation of economies of scale and the firm can further expand its output level.

Answer:

The production function explains the relationship between input and output. On the other hand, cost function explains the relationship between cost and output. As the output increases, the cost function and production function gives increasing returns to scale (output greater than input) and after sometime these functions start giving decreasing returns to scale (output less than input and cost greater than output). Therefore, the costs function and production function has a direct relationship.