MSA Computer Corporation manufactures three models of computers: the Alpha4, Beta5, and the Delta6. The firm employs

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MSA Computer Corporation manufactures three models of
computers: the Alpha4, Beta5, and the Delta6. The
firm employs thirteen technicians working 160 hours each per month
on its assembly line. Management insists that no more than
full employment on the assembly line (i.e., all 160 hours of time)
can be maintained for each worker during next month’s operations,
so there will be no overtime. It requires 20 labor hours to
assemble each Alpha4 computer, 25 labor hours for each Beta5 model,
and 15 hours for each Delta6. Final testing and inspection
requires 3 hours for each Alpha4, 1.5 hours for each Beta5, and 1.2
hours for each Delta6. In addition to the workers on the
assembly line, the company has up to 80 hours available for
inspection and testing each month. Demand is such that the
company can and will sell all of the computers that it
produces. MSA must produce at least 10 Delta6
computers. In addition, the number of Alpha4 computers
produced each month must equal or exceed the combined total of
Beta5 and Delta6 computers produced. Alpha4 computers
generate $1,200 profit per unit, Beta5 computers yield $1,800 each,
and Delta6 computers yield $1,000 per unit. If the
optimal answer is in fractions of computers, leave them as
fractions.
a) Formulate the linear programming problem to maximize
the profit during the coming month. Provide the variables
being used, the objective function and all of the constraints that
are indicated by the above description of the
problem.
b Instead of the constraint that requires that MSA must produce
at least 10 Delta6 computers, suppose it is now required that no
more than 35% of the computers produced must be Delta6
computers. Write the constraint to express this
relationship. You do not need to resolve the revised linear
programming formulation for the optimal
answer.