Question 11

A company makes two products, X and Y. Product X has a contribution of 124 per unit and product Y 80 per unit. Both products pass through two departments for processing and the times in minutes per unit are:

	Product X	Product Y
Department 1	150	90
Department 2	100	120

Currently there is a maximum of 225 hours per week available in department 1 and 200 hours in department 2. The company can sell all it can produce of X but EU quotas restrict the sale of Y to a maximum of 75 units per week.

The company, which wishes to maximize contribution, currently makes and sells 30 units of X and 75 units of Y per week.

The company, which wishes to maximize contribution, currently makes and sells 30 units of X and 75 units of Y per week.

The company is considering several possibilities including:

1. altering the production plan if it could be proved that there is a better plan than the current one;
2. increasing the availability of either department 1 or department 2 hours. The extra costs involved in increasing capacity are 0.5 per hour for each department;
3. transferring some of its allowed sales quota for Product Y to another company. Because of commitments, the company would always retain a minimum sales level of 30 units.

You are required to:

1. calculate the optimum production plan using the existing capacities and state the extra contribution that would be achieved compared with the existing plan;
2. advise management whether it should increase the capacity of either department 1 or department 2 and, if so, by how many hours and what the resulting increase in contribution would be over that calculated in the improved production plan;
3. calculate the minimum price per unit for which it could sell the rights to its quota, down to the minimum level, given the plan in (a) as a starting point.