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2. A Singapore company manufactures 50-inch and 75-inch rear projection televisi

ID: 466241 • Letter: 2

Question

2. A Singapore company manufactures 50-inch and 75-inch rear projection television sets. Each 50-inch set contributes $225 to profits and each 75-inch set contributes $495 to profits. The company has purchase commitments for 400 50-inch sets for the next month. Although they think they can sell all the 50-inch sets that they could currently make, they do not think they can sell more than 375 75-inch sets. Their factory capacity allows them to make only 975 sets of both sizes total. Formulate as a linear programming problem.

Explanation / Answer

Decision variable:

Let,

X1 = number of 50-inch projection television to be produced by manufacturer

X1 = number of 75-inch projection television to be produced by manufacturer

Objective Function:

The objective is to maximize the profit by producing both the televisions. The profit function is given as:

Max. Z = $225X1 + $495X2

Constraint:

Various constraints that manufacturer faces are as follows:

Capacity Constraint: Maximum capacity available for both the televisions is 975 units

X1 + X2 975

Demand Constraint for 75-inch Televisions: Maximum Sell of the Television is 375 units

X2 375

Demand Constraint for 50-inch Televisions: As there is an order of 400 sets and all that are produced can be sold in market, then the manufacturer has to produce minimum 400 sets.

X2 400

Non-Negativity constraint: The sets produced cannot be in negative numbers.

X1, X2 0