Question

Exercise 3 LP 3. Amanufacturer wants to maximize the profit of two products Product X yields a profit of $ 2.50 per unit, and product Y yields a profit of $3.20 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 is no more than half the demand for product X. The production level of product X is less than or equal to 600 units plus three times the production level of product Y. Show all steps. Answer the question fully! Use and show how systems of equations obtain critical corners!

Answer 1

Ans: Maximize the profit of two products:

Calculations are hand written:

And = Maximize profit of two products = ? Product X = x Product Y = y → Total Production Level Constecairt :- xty <= 1200 Demand Equation in y = + x x (2 y Production Level :- → X =< 600 +34 X =< 3(200 +y) y 200 ty >= 2 y> : 1 - 200 3 3 - Calculation : + 2 += 1200 y = 1200- 4) y n = 600+ 3y x = 600 + 3600 - 3x 2+3x - 4200 4x=4200 x = 1050

→ Subolitute x = 1050 in Equation X=600 + 3y :- x=600+ +3y 1050 - 600 +3y 1050 - 600 = 34 450 =y 3 y = 150 y If Demand equal to product x all sold :- - ” [Equation 2] y 2 Y= 1050 [Pething x = 1050] y = 525 The projet generated according to the demand calculated :- -Y U - 1050 X $2.50 x = $ 2625 y y = 150 x $ 3.20 Y - $ 480 Total x+y = $3105

Product X = $2,625

Product Y = $ 480

Total = $3,105