Final answer:
The firm did not produce at a price of $5 but started producing when the price increased to $10, suggesting that the minimum value of the firm's average variable cost is between $5 and $10.
Step-by-step explanation:
From the provided information, we can infer that the firm's average variable costs and fixed costs combined are such that it is not profitable for the firm to produce at a price of $5. However, when the price rises to $10, the firm is able to cover its variable costs and some portion of its fixed costs, making it profitable to produce 100 tons. We can deduce that the minimum value of the firm's average variable cost lies between $5 and $10, since the firm chose not to produce when the price was at $5 but did produce when the price increased to $10. This indicates the firm has reached or surpassed the breakeven point on the variable costs at the higher price. Thus, the correct answer is:
e. the minimum value of the firm's average variable cost lies between $5 and $10.