Final answer:
The tire store needs to estimate the optimal number of tires to order using the newsvendor model and the critical ratio, but without explicit formulas or ratios, the exact number cannot be determined in this context.
Step-by-step explanation:
The tire store has to determine the optimal stock quantity that accounts for regular demand variability and the cost of overstocking. With a mean annual demand of 1,000 tires and a standard deviation of 50, a normally distributed demand implies that actual demand will fall within plus or minus one standard deviation from the mean about 68% of the time, and within plus or minus two standard deviations about 95% of the time.
To decide the number of tires to order without incurring significant overstock costs, the store can use the newsvendor model, taking into account the cost of underordering (losing potential profit from selling at $130) and the cost of overordering (losing $10 per tire when selling the excess at $90). To compute the optimal order quantity, we should calculate the critical ratio, which is the cost of underordering divided by the total cost (the sum of underordering and overordering costs). The critical ratio can then be used to find the corresponding z-value in the standard normal distribution, which can then be multiplied by the standard deviation and added to the mean demand to find the optimal stock level.
However, without explicit formulas or a given critical ratio, we cannot determine the exact number of tires to be ordered. The tire store manager would typically use inventory management software or consult with a statistician to perform these calculations accurately.