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A sudden increase in the demand for smoke detectors has left Acme Alarms with insufficient capacity to meet demand. The company has seen monthly demand from its retails for its electronic and batter-operated detectors rise to 20,000 and 10,000 respectively. Acme’s production process involves three departments: fabrication, assembly and shipping. The relevant quantitative data on production and prices are summarized as follows:

Monthly Hours Hours/Unit Hours/Unit
Department Available (Electronic) (Battery)

Fabrication 2,000 0.15 0.1
Assembly 4,200 0.2 0.2
Shipping 2,500 0.1 0.15

Variable Cost/Unit $18.80 $16.00
Retail Price $29.50 $28.00

The company also has the option to obtain additional units from a subcontractor, who has offered to supply up to 20,000 units per month in any combination of electric and battery-operated models, at a change of $21.50 per unit. For this price, the subcontractor will test and ship its models directly to the retailers without using Acme’s production process.

a. What are the maximum profit and the corresponding make/buy levels? (Fractional decisions are acceptable.)
b. Suppose that Acme requires that the solution provided by the model be implement able without any rounding off. This I, the solution must contain integer decisions. What are the optimal make/buy levels?
c. Is the solution in part (b) rounded-off version of the factional solution in para(a)?