HTC makes two types of handheld devices: smartphones and tablet pcs. These devic
ID: 431606 • Letter: H
Question
HTC makes two types of handheld devices: smartphones and tablet pcs. These devices are designed to run only one operating system either google's android or microsoft operating system. the company want to limit production to a maximum of 250 thousand android based devices and 350 thousand microsoft based devices. additional info is given below. the objective is to determine the optimal quantities to produce for each type in order to maximize profit. Formulate mathematical problem. Do not solve.
Androdid o.s microsoft o.s production capacity budget to cover costs smart phpne cost: 150/unit cost:$200/unit 300 thousand unit for any combiation andriod/microsoft 45 million for any combination andriod/microsoft profit: 48/unit prpfit:55/unit Tablet Pc cost 135/unit cost:180/unit 250 thousand for any combination android /microsoft 36 million for any combination/microsoft profit 65/unit profit:70/unitExplanation / Answer
Let the optimum quantities to be produced to maximize profit :
Smart phone android based = Sa
Smart phone Microsoft based = Sm
Tablet PC Android based = Ta
Table PC Microsoft based = Tm
Provided ,
Sa, Sm, Ta, Tm > = 0
Since the objective is to maximize profit,
The Objective function :
Z = Maximize( 48.Sa + 55.Sm + 65.Ta + 70.Tm)
Constraints :
Sa + Sm < = 300,000
Ta + Tm < = 250,000
150.Sa + 200.sm < = 45,000,000
135.Ta + 180..Tm < = 36,000,000
5. since company wants to restrict Android based devices to a maximum of 250,000 thousands,
Sa + Ta < = 250,000
6.Since company wants to restrict Microsoft based devices to a maximum of 350,000 thousands
Sm + Tm < = 350,000
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