The Can Division of Sheffield Corp. manufactures and sells tin cans externally for $0.60 per can. Its unit variable costs and unit fixed costs are $0.24 and $0.06, respectively. The Packaging Division wants to purchase 50,000 cans at $0.30 a can. Selling internally will save $0.03 a can.
Required:
1. Assuming the Can Division is already operating at full capacity, what is the minimum transfer price it should accept?

Minimum transfer price  =$ 0.57

Explanation:

The Can Division of Sheffield Corp is already operating her full capacity,

This implies that it call sell all it can produce to external buyers, to remain indifferent it will have have to make the same amount of contribution from internal sales it would from external.

Therefore the minimum transfer price:

Minimum transfer price= Variable cost - internal savings in variable cost  + contribution from external sales

Savings in variable cost = $0.03

Contribution from external sales = $0.60 - $0.24 = $0.36

The minimum transfer price would be equal

Minimum transfer price = 0.24 - 0.03  + 0.36 = 0.57

P(x)=-30x^2+9000x-567000

Explanation:

First, we need to remember the parts of a Profit function. A profit a business makes  equals revenue (R(x)) minus its costs (C(x)). So

There are two parts

1. Revenue: which is equal to the number of units sold times the price:

where x is the price you charge and Q(x) is the number of shirts that can be sold. Then

2. Cost. The cost function is directly given by the question

Putting this together we have