The Case study is about Liner Programming Liner Programming Case Study Nutty Nuts Company produces three nut mixers: Regular, Deluxe and Holiday. Currently Nutty Nuts has purchased the following shipments of nuts at the prices shown Type of Nut Shipment Amount (lbs) Cost per Shipment Almond 6000 7800 Brazil 7500 7350 Filbert 7500 6750 Pecan 6000 7260 Walnut 7500 7875 The Regular Mix consists of 15% almonds, 25% Brazil nuts, 25% filberts, 10% pecans, and 25% walnuts. The Deluxe Mix consists of 20% of each type of nuts, the Holiday Mix consists of 25% almonds, 15% Brazil nuts, 15% filberts, 25% pecans, and 20% walnuts. Nutty Nuts' accountant analyzed the cost of packaging materials, sales price per pound, and so forth, and determined that the profit contributions per pound is $1.65 for the Regular Mix, $2.00 for the Deluxe Mix, and $2.25 for the Holiday Mix. These figures do not include the cost of specific types of nuts in the different mixes because that cost can vary greatly in the commodity markets. Nutty Nuts already received orders of 10,000 pounds of Regular Mix, 5000 pounds of Deluxe Mix and 3000 pounds of Holiday Mix. Because demand is running high, Nutty Nut expects to receive many more orders than can be satisfies. Nutty Nuts is committed to using the available nuts to maximize profit over the fall season; nuts not used will be given to the Free Store. Even if it is not profitable to do so, Nutty Nut president indicated that the orders already received must be satisfied. Managerial Report Perform analysis of Nutty Nuts' product mix problem, and prepare a memo (no more than 2 pages) for Nutty Nuts' president that summarizes your findings and recommendations. In the Appendix, be sure to include your analysis on the following: 1. The cost per pound of the nuts included in the Regular, Deluxe and Holiday mixes. 2. The optimal product mix and the total profit contribution 3. Recommendations regarding how the total profit contribution can be increased if additional quantities of nuts can be purchased 4. A recommendation as to whether Nutty Nuts should purchase an additional 1000 pounds of almonds for $1000 from a supplier who overbought 5. Recommendations on how profit contribution could be increased (if at all) if Nutty Nut does not satisfy all existing orders. This is a Linear Programming Problem to Maximise the prot, by satisfying the constraints The Objective function is to Maximise Max Z = 'l.E-5x1+2x2+2.25x3 [Prot from Regula, Deluxe and Holiday Mix are $1.55, $2, $2.25 respectively} Subject to [1.1 Ext +.2x2+.25x3<:= [Almond Constrain} [15% =EI.15, ] [1.25x'l +_2x2+_'l 5x3c=TEUU [Brazil Nut} U.25x'l+_2x2+_'l5x3c=T5EIEI [Filbert Nut} [1.1Ux'l +_2x2+_25x3c= [Pec an} [1.25x'l +_2x2+_20x3-=:=TEUU {Walnut} x1s=1 [Demand for Regular} K23: 3000 [Demand For Deluxe} K33: 5000 [Demand For Holiday MIX} K1,K2,K3:==EI No constrains is required for cost of shipment, because already purchased The solution to be problem, by LPP through MS Excel Solver Application are III I - I II II II ---- III II II II II II II I I 'IEIELEE BEIEIEI E E 1L if ADDIWDNAL 1555 ALMONDS BOUGHT THEN SOLUTION, IS Mesa: E 55333-33 1'ul'eriehl e Regular x1 11555.5T Deluxe x2 'ITEH 5-5T x3 5555 Helid a}; Gen etraint V V V .-"'-. .-"'-. .-"'-. .-"'-. a". || || || || || || || 5 5553.333 T555 T255 T555 T255 T555 5555 5555 T555 T555 11555-5T 1555 1T5'15_5T 3555 5555 5555 this is a linear progamming poblem to maximise pofit by satifying te constraints the objective function is to maximise max z=1.65x*1+4+2.25*3 (pofit from regula delux and holiday mix are $1.65,$2,$2.25,espectively subject to 0.15*1+0.20*2+0.25*3=6000(almond constraint ) 0.25*1+0.20*2+0.15*3=7500(brazil nut ) 0.15*1+0.20*2+0.25*3=7500(filbet nut ) 0.10*1+0.20*2+0.25*3=6000(pecan ) 0.15*1+0.20*2+0.25*3=6000(wilber ) x1=1000(Demand for regular ) x2=3000 (demand for deluxe) x3=500(demand for holiday mix) x1,x2,x3=0 no constraints is requied for cost of shipment because already purchase ,the solution by lpp MS excel solver are regular delux holiday MAX Z= 61375 VARIABLE x1 x2 x3 17500 10625 5000 constraint 6000 6000 <= 7250 7500 <= 7250 7500 <= 5125 6000 <= 7500 7500 <= 17500 1000 <= 10625 3000 <= 5000 5000 <= if additional 1000 almonds bought then solution is MAX Z= 66333.33 regular delux holiday VARIABLE x1 x2 x3 constraint 6583.33 7250 7250 6000 11666.67 17916.67 5000 7000 <= 7500 <= 7500 <= 6000 <= 7500 11666.67 17916.67 5000 7500 <= 1000 <= 3000 <= 5000 <= lpp MS excel solver are