SnackNation is deciding what to produce in the upcoming month. Due to past purch

Question

SnackNation is deciding what to produce in the upcoming month. Due to past purchases, they have 500 lbs.of walnuts, 1000 lbs. of peanuts, and 500 lbs. of chocolate. They currently sell three mixes: Trail Mix, which consists of 1 lb of each material; Nutty Crunch, which has 2 lbs. of peanuts and 1 lb of walnut; and Choc-o-plenty, which has 2 lbs. of chocolate and 1 lb of peanuts. They can sell an unlimited amount of these mixes, except they can sell no more than 100 units of Choc-o-plenty. The income on the three mixes is $2, $3, and $4, respectively. The problem of maximizing total income subject to these constraints is the following:

Using the above tableau, determine the following:

(a) What is the solution represented by this tableau (both production quantities and total income)? How do we know it is the optimal tableau?

(b) Suppose the income for Trail Mix (x1) is only an estimate.
For what range of values would the basis given by the above tableau still be optimal?
What would be the solution (both production quantities and total income), if the income was only $2.75?

(c) How much should SnackNation willing to spend to procure an extra pound of peanuts? How about an extra pound of walnuts?
How about an extra pound of chocolate?

(d) For what range of peanut stock values is the basis given by the above tableau still optimal?
What would be the solution (both production quantities and total income) if there were only 900 lbs of peanuts available?

(e) A new product, Trail Booster, consists of 1 lb of each of peanuts and chocolate, and 2 lbs of walnuts. What income do we need to make on this product in order to consider producing it?

Maximize 2 1 3r2 4r3 Subject t 1 2 00 1 2a2 1000 1 3 00 100 i 0 for all i The optimal tableau for this problem is after adding slacks for the four constraints RH 0 0 0 1 1 0 3 1300 0 0 0 2 -1 0 1 100 0 1 0 -1 1 0 -1 400 0 0 0 -2 1 3 200 0 0 0 0 0 1 100

Explanation / Answer

Solution represented by this tableau is

x1 = 100

x2 = 400

x3 = 100

and total income = 200 + 1200 + 400 = $1800

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