An electronics rm is producing three lines of products for sale to the government: transistors, micromodules, and circuit assemblies. The firm has four physical processing areas designated as follows: transistor production, circuit printing and assembly, transistor and module quality control, and circuit assembly test and packing. The various production requirements are as follows: Production of one transistor requires 0.1 standard hour of transistor production area capacity, 0.5 standard hour of transistor quality control area capacity, and $0.70 in direct costs. Production of micro-
modules requires 0.4 standard hour of the quality control area capacity, three transistors, and $0.50 in direct costs. Production of one circuit assembly requires 0.1 standard hour of the capacity of the circuit printing area, 0.5 standard hour of the capacity of the test and packing area, one transistor, three micromodules, and $2.00 in direct costs.

Suppose that the three products (transistors, micromodules, and circuit assemblies) may be sold in unlimited quantities at prices of $2, $8, and $25 each, respectively. There are 200 hours of production time open in each of the four process areas in the coming month. Formulate a mathematical model to help determine the production that will produce the highest revenue for the firm.

a. Identify the decision variables: What decision is to be made?

b. Formulate the objective function: How do these decisions affect the objective?

c. Formulate the constraint set: What constraints must be satisfied? Be sure to consider whether negative values of the decision variables are allowed by the problem, and ensure they are so constrained if required.