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# (Solved): solve correctly please O1. A retail store stocks three types of shirts $$\mathrm{X}, \mathrm{Y} ... ?solve correctly please O1. A retail store stocks three types of shirts \( \mathrm{X}, \mathrm{Y}$$ and $$\mathrm{Z}$$. These are packed in attractive cardboard boxes. During a week the store can sell a maximum of 350 shirts of type $$X$$ and a maximum of 200 shirts of type $$Y$$ and $$Z$$. The storage capacity, however, is limited to a maximum of 450 of all types combined. Type $$\mathrm{X}$$ shirt fetches a profit of Rs. 3/- per unit, type Y a profit of Rs. 4/- per unit, and type Z a profit of Rs. 2/- per unit. How many of each type the store should stock per week to maximize the total profit? Formulate a mathematical model of the problem. Q2. Considering the following problem: $\begin{array}{ll} \text { Maximize } Z= & 50 x_{1}+80 x_{2} \\ \text { subject to: } & x_{1}+x_{2} \leq 20 \\ & 5 x_{1}+2 x_{2} \leq 60 \\ & x_{1} \leq 10 \\ & x_{1}, x_{2} \geq 0 \end{array}$ 1. Trace the constraints in the Coordinate Axes 2. Locate the Feasible Solution Area 3. Calculate $$\mathrm{Z}$$ in the Border points (Extreme points) 4. Find the Optimal Solution 5. Write the problem in standard form 6. Calculate Slack or Surplus 7. Which constraints are binding, non-binding? Why?

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