(a) Formulate the above problem as a linear optimization model. (b) Solve the linear optimization model graphically. Plot the constraints, and identify each constraint and the feasible region. Describe the optimal solution. Which constraints are binding at the optimal solution? What is the value of the objective function at the optimal solution?
The Magnetron Company manufactures and markets microwave ovens. Currently, the
company produces two models: full-size and compact. Production is limited by the
amount of labour available in the general assembly and electronic assembly
departments, as well as by the demand for each model. Each full-size oven requires 2
hours of general assembly and 2 hours of electronic assembly, whereas each compact
oven requires 1 hour of general assembly and 3 hours of electronic assembly. In the
current production period, there are 500 hours of general assembly labour available and
800 hours of electronic assembly labour available.
In addition, the company estimates that it can sell at most 220 full-size ovens and 180
compact ovens in the current production period. The earnings contribution per oven is
$120 for a full-size oven and $130 for a compact oven. The company would like to find
an earnings-maximizing production plan for the current production period.
(a) Formulate the above problem as a linear optimization model.
(b) Solve the linear optimization model graphically. Plot the constraints, and identify
each constraint and the feasible region. Describe the optimal solution. Which
constraints are binding at the optimal solution? What is the value of the objective
function at the optimal solution?
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