2) Max Z = x1 + X2 s.t. 2x1 + 4x2 ≤ 14 6x1 + 2x2 ≤ 12 Xi≥ 0 Study the coefficients of the variables in the objective function of each problem. These represent the profit contributions of products X₁ and x2 in each problem. Try to understand intuitively why the optimal solution is changing for each problem (at a different corner point).

Suppose that the revenue and cost functions for a particular company are given by R(x) = – 3x² + 20x, C(x)=2x+ 15. What is the number of items x the company must sell in order to maximize profit?

The Pear company sells pPhones. The cost to manufacture x pPhones is C(x): 22x51000x + 20390 dollars (this includes overhead costs and production costs for each pPhone). If the company sells x pPhones for the maximum price they can fetch, the revenue function will be R(x): 29x² + 163000x dollars. 2 = X= How many pPhones should the Pear company produce and sell to maximimze profit? (Remember that profit=revenue-cost.)

Maximize z = 2x1 + 7x2 + x3 , subject to 2x1 + 7x2 + x3 ≤ 103 4x1 + x2 + 11x3 ≤ 239 with x1 ≥ 0, x2 ≥ 0 , x3 ≥ 0