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Force Completion This test can be saved and resumed at any point unil tie has expired The timer will continue to nun i you leave the test Remaining Time: 27 minutes, 37 seconds. Question Completion Status: QUESTION 1 Farmes Jones bakes two types of cake (Chocolate and vanailla) to supplement his income. Each chocolate cake can be sold for $5, and each vanilla cake can be sold for $3. Each chocolate cake requires 30 minutes of baking time and whes 3 eges. Each vanill cake requires 40 mirutes of baking time and uses 2 eges At most 4 hours of baking time and 18 eggs are available everyday Let x number of chocolate cakes to bake, y- number of vanilla cakes to bake. Using these decision variables, formulate an LP to maximize Farmer Jones’ revenue In the LP model, the objective function is The conatzaint enforeing the upper linit for baking time is The sign reatrictions are x 2and y 2 o vanilla cakes, and his maxi-revenue is – Graphically solving thisproblem, we obtain that Famer John can maximize his revenue by baking chocolate cakes and QUESTION 2 30 15
Expert Answer
Q2.
max 5x + 3y
Subject to,
30x + 40y <= 240
3x + 2y <= 18
x >=0; y>= 0
Solution: x = 6; y = 0, Max revenue = 30
Q2.
The above two constraints will only be applicable.
Q.
If we solve the LP, we will get x1=12 and x2=0 as optimal solution
3×1 + 2×2 = 36 (equal to RHS) so, 3×1 + 2×2 <= 36 is a binding constraint
3×1 + 4×2 = 36 (less than RHS) so, 3×1 + 4×2 <= 48 is a nonbinding constraint
x1 >= 0 is nonbinding and x2 >= 0 is binding
Q4.
Optimal solution, x1 = 0, x2 = 12, and Z = 0 + 2*12 = 24
