1. Alternative Formulation:
First define the following additional variables:
wC= weigh of tomato grade C allocated to produce whole tomatoes (lbs),jC=weight of tomato grade C allocated to produce tomato juice (lbs),
pC=weight of tomato grade C allocated to produce tomato paste (lbs).
The update formulation is then:
Maximize((1.20+3.24)*100)/18)*(wA+ wB + wC) + ((0.36+3.60)*100)/20)*( jA+ jB+ jC) + ((1.05+4.50)*100)/25)*( pA+ pB+ pC)
9wA+ 6wB +3wC ≥ 8(wA+ wB +wC) wA - 2wB - 5wC ≥ 0 (whole tomatoes quality constraint)
9jA+ 6jB +3jC ≥6(jA+ jB +jC) jA - jC ≥ 0 (tomato juice quality constraint)
wA+ wB + wC ≤ 800,000*18 (whole tomatoes production less than demand)
jA+ jB + jC ≤ 50,000*20 (tomato juice production less than demand)pA+ pB + pC ≤ 80,000*25 (tomato paste production less than demand)
wA+ jA+ pA ≤ 600,000 (grade A tomatoes usage less than available amount)
wB+ jB+ pB ≤ 1,600,000 (grade B tomatoes usage less thanavailable amount)
wC+ jC+ pC ≤ 800,000 (grade B tomatoes usage less than available amount)
wA, wB, wC, jA, jB, jC, pA, pB , pC ≥ 0
The new model solution puts all 800 thousand lbs. of Grade Ctomatoes into Paste (see spreadsheet)
2. The income from selling the tomatoes is $685,000 (from the Excel spreadsheet solution). The cost of the tomatoes used is $0.18*3,000,000 = $540,000. The netincome is $145,000.
3. First make sure to change the formatting of the Shadow price column to allow for 3 decimal places. The shadow price for Grade A tomato supply is 27.1 cents/lb. and theallowable increase is 200 thousand lbs. This means a purchase of 80,000 lbs. at 25.5 cents/lb. should be undertaken
4 From the Sensitivity Report below, the shadow price on the Paste demand constraintis $0.024/lb and the allowable increase is 100 thousand lbs. The proposed increase is 3 thousand cases @25 lbs per case or 75 thousand lbs. which is within the allowable increase. Red Brand would...