Question

National Business Machines manufactures x model A portble printers and y model B portable printers. Each model A costs $100 to make, and each model B costs $150. The profits are $45 for each model A and $30 for each model B portable printer. If the total number of portable printers demanded per month does not exceed 2500 and the companu has earmarked no mote than $600,000/month for manufacturing costs, how many units of each model should National make each month to maximis its monthly profit ?

(x, y) =

what is the optimal profit? $

Answer 1

Let,

x = No of 'A' type portable printers

y = No of ‘B' type portable printers

The liner inequalities affording to the given constraints are,

• Cost Constraint [100x + 350y ≤ 600,000]

• Production Constraint [x + y ≤ 2500]

To find the common point of intersection let us write these inequalities as a system of linear equations, these intersection will represent the optimal production amount for these given constraints.

Equation no1: 100x +350y=600,000

Equation no2: x + y = 2500

Now, let's multiply each term in Equation no2 and solve these linear equations by using Elimination method.

  

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' B ' type printers

x + y = 2500 (Equation no 2)
x + 1400 = 2500

x = 2500 - 1400

x = 1100 ‘A' type printers

Therefore , (x,y) = (1100,1400)

Now, let's find out the optimum profit by substituting in our optimal values (x,y) into the equation of profit.
Profit = 45x + 35y
Profit = 45(1100) + 35(1400)

Profit = 43,500 + 49,000

Profit = 92,500

Optimal Profit = $92,500