Question

A manufacturer wants to maximize the profit of two products. Product I yields a profit of $ 1.50 per unit, and product II yields a profit of $2.00 per unit. Market tests and available resources have indicated the following constraints: • The combined production level should not exceed 1200 units per month. • The demand for product II is no more than half the demand for product I. • The production level of product I is less than or equal to 600 units plus three times the production level of product II. Solve the application. (Be sure to show the Objective function, Constraints, the feasible region, vertices and optimal solution.)

Answer 1

Let for product 1 =X and product 2 =Y

P=combined profit its called the objective function .

objective function

constraints

.....1

............ 2  

.......3

......4

......5

by solving the equction we get maximise profite ,We use the value of x and y in equction of P .

for(0,0) P=1.5(0)+2(0)=0

for(800,400) P=1.5(800)+2(400)=2000

for(1050,150) P=1.5(1050)+2(150)=1875

for(600,0) P=1.5(600)+2(0)=900

so max profite is 2000 for product i st 800 unit and product 2nd 400 unit .