ABC company currenly has 2 products , Product X and Product Y.The company is experiencing a problem , it and can only spend a limited amount of time to inspect the product in order to find the problem (the company wants to fix the problem consider about constraint for now). Here is the information, each Product X requires 11 minutes to inspect, while eachProduct Y requires 12 minutes for inspection. Currently, ABC company is producing 101 units of Product X and 130 units of Product Y per week. Inspection costs $32 per hour. Also, there are$4507 per week in fixed costs, $13 per units in variable costs for Product X, and $11 per unit in variable costs for Product Y. Fixed costs are allocated to the product based on units produced. Product X sells for $28 per unit, and Product Y sells for $26 per unit.

1. Assume that inspection time is fully utilized. Calculate the shadow cost of an hour of inspection time.

2. Briefly explain why it is relevant that inspection time is fully utilized in the prior question.

3.

Ignore the information in question 1 and now assume the shadow cost is $51 per hour. For Product Y, assume allocated fixed costs of $1224 and variable costs of $14 per unit. Product Y uses 0.16 hours of inspector time per unit and has a demand curve of V = 1000 - 30P.

What is the optimal price to charge for product Y?