Originally Posted by

**ticbol** Let me assume you know simple (not simplex) linear programming.

Regular spread, R = 75% Mild(M) and 25% Sharp(S)

Zesty spread, Z = 55% M and 45% S

So,

M = 0.75R +0.55Z

S = 0.25R +0.45Z

M <= 8000 lbs

S <= 3500 ibs

So,

0.75R +0.55Z <= 8000 -----------constraint (1)

0.25R +0.45Z <= 3500 -----------constraint (2)

Or, multiplying (1) and (2) by 20,

15R +11Z = 160,000 --------------(1a)

5R +9Z = 70,000 -----------------(2a)

R > 0, and Z > 0 -------------non-zero (because there should be R or Z), non-negative constraints.

Plot those on the same (R,Z) rectangular axes, in lbs.

Intersection of (1a) and (2a) is point (8375,3125)

The feasible region is the quadrilateral bounded by (1a), (2a) and the R and Z axes. The optimum point can only be (8375,3125).

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a) how many containers of Regular and Zesty should NEC produce?

1 container = 12 oz.

1 pound = 16 oz.

Regular spread = (8375*16)/12 = 11,166.67 containers .............answer.

Zesty spread = (3125*16)/12 = 4,166.67 containers ................answer.

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b) What is the optimal profit?

(b.1) Total Cost:

Mild cheddar ========> [0.75(8375) +0.55(3125)](1.30) = $10,400.

Sharp cheddar =======> [0.25(8375) +0.45(3125)](1.50) = $5,250.

Blending and packaging ==> [11,166.67 +4,166.67](0.30) = $4,600.

So, Total Cost = 10,400 +5250 +4600 = $20,250

(b.2) Total Revenue:

Regular spread ==> (11,166.67)(2.15) = $24,008.34

Zesty spread =====> (4,166.67)(2.35) = $9,791.67

So, Total Revenue = 24,008.34 +9,791.67 = $33,800.

Therefore, optimal profit = 33,800 -20,250 = $13,550 .......answer.