A firm produces an item of two types: for the high-end market and for the mass market. Both products require the same type of raw materials but in different proportions. For each ton of output produced, the required resources expressed in hours are as follows in Table 4:

 The firm employs eight people in the workshop, three machines of Type A and two machines of Type B. The working hours are 8 h per day for 25 days in a month. The hours available are therefore 1600 person hours, 600 machine hours A and 400 machine hours B. The contribution margin for each ton produced is £600 for the massmarket product, while £ 1050 for the high-end product:

a. Identify the objective function, formalize the various constraints, and determine the most profitable product vector mix.

b. Represent the linear problem geometrically in a chart.

Transcribed Image Text:

TABLE 4 Mass market High-end market Person-hours Machine-hours A Machine-hours B 1.0 1.8 0.5 0.6 0.3 0.2