Siyi Ltd is a specialist engineering firm that makes four products, for which the following information is available:

A B C D

Selling price per unit 100 64 54 62

Variable cost per unit 50 40 42 30

Weekly demand (units) 40 70 50 80

Machine hours per unit 5 2 3 4

Due to a recent market boom, demand is now outstripping the capacity of its plant, which is constrained to 500 hours machine time per week. In the medium-term, the management will consider expanding capacity but there remains a short-term problem of how to allocate the available capacity among the four products.

Required:

A) Determine the optimising plan for using the available machine hours in the short-term, and calculate the maximum achievable contribution.

B) Calculate the shortfall in contribution imposed by the constraint on machine hours, the maximum contribution in the absence of a machine hour constraint, and how many additional machine hours are required.