# please do exercies #9 and #4

**Question description**

Taha, Exercise Set 2.2a, #9: Define decision variables, objective function and constraints, and solve graphically.

9.) ChemLabs uses raw materials *I* and *II* to produce two domestic cleaning solutions, A and B. The daily availabilities of raw materials *I* and *II* are 150 and 145 units, respectively. One unit of solution A consumes .5 unit of raw materials *I* and .6 unit of raw material *II*, and one unit of solution B uses .5 unit of raw material *I* and .4 unit of material II. The profits per unit of solutions A and B are $8 and $10, respectively. The daily demand for solution A lies between 30 and 150 units and that for solution B between 40 and 200 units. Find optimal production amounts of A and B.

–Taha, Exercise Set 2.4e, #4: Formulate the problem only. Define decision variables, objective function and constraints. You do NOT need to solve the problem; formulate only!

4.) A refinery manufacturers two grades of jet fuel, F1 and F2, by blending four types of gasoline, A,B,C and D. Fuel F1 uses gasolines A,B,C and D in the ratio 1:1:2:4 and fuel F2 uses the ratio 2:2:1:3. The supply limits for A,B,C and D are 1000,1200,900,and 1500 bbl/day ,respectively the cost per bbl for gasolines A,B,C,and D are $120, $90 , $100 and $150, respectively. Fuels F1 and F2 sell for $200 and $250 per bbl, respectively. The minimum demand for F1 and F2 is 200 and 400 bbl/day, respectively. Develop an LP model to determine the optimal production mix for F1 and F2 and find the solution using AMPL, Solver or TORA.

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