The Sun food co. produces three canned fruit products. The mail ingredients in each product are pears and...

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The Sun food co.produces three canned fruit products. The mail ingredients in eachproduct
are pears and peaches. Eachproduct is produced in lots and must go through three processes-
mixing, canning, andpackaging. The resource requirements for each product and eachprocess
are shown in the following LPformulation.
Maximize Z = 10 x1 + 6 x2 + 8x3 (profit, $)
subject to
20 x1 + 10 x2 + 16 x3 <= 320 (pears, lbs)
10 x1 + 20 x2 + 16 x3 <= 400 (peaches, lbs)
   x1 + 2 x2 + 2 x3 <= 43 (mixing,hr)
   x1 +    x2+    x3 <= 60 (canning, hr)
2 x1 +    x2 +    x3<= 40 (packaging, hr)
x1, x2, x3 >= 0 (non-negativity conditions)
A) What is the maximum price the company would bewilling to pay for additional pears?
How much could be purchased at that price?
B) What is the marginal value of peaches? Over whatrange is this price valid?
C) The company can purchase a new mixing machine thatwould increase the available
mixing time from 40 to 60 hours. Would this affectthe optimal solution?
D) The company can also purchase a new packagingmachine that would increase the available
packaging time from 40 to 50 hours. Would yourecommend this? Explain.
E) If the manager were to attempt to secure additionalunits of only one of the resources,
which should it be and why?

Answer & Explanation Solved by verified expert

4.5 Ratings (919 Votes)

Solution using Solver is as followsFormulaE2 SUMPRODUCTB2D2B9D9 copy to E2E7Sensitivity report is as underA Refer sensitivity report Shadow price of pear constraint is0467 Therefore Maximum See Answer

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The Sun food co.produces three canned fruit products. The mail ingredients in eachproduct
are pears and peaches. Eachproduct is produced in lots and must go through three processes-
mixing, canning, andpackaging. The resource requirements for each product and eachprocess
are shown in the following LPformulation.

Maximize Z = 10 x1 + 6 x2 + 8x3 (profit, $)
subject to
	20 x1 + 10 x2 + 16 x3 <= 320 (pears, lbs)
	10 x1 + 20 x2 + 16 x3 <= 400 (peaches, lbs)
	x1 + 2 x2 + 2 x3 <= 43 (mixing,hr)
	x1 + x2+ x3 <= 60 (canning, hr)
	2 x1 + x2 + x3<= 40 (packaging, hr)
	x1, x2, x3 >= 0 (non-negativity conditions)

A)	What is the maximum price the company would bewilling to pay for additional pears?
	How much could be purchased at that price?
B)	What is the marginal value of peaches? Over whatrange is this price valid?
C)	The company can purchase a new mixing machine thatwould increase the available
	mixing time from 40 to 60 hours. Would this affectthe optimal solution?
D)	The company can also purchase a new packagingmachine that would increase the available
	packaging time from 40 to 50 hours. Would yourecommend this? Explain.
E)	If the manager were to attempt to secure additionalunits of only one of the resources,
	which should it be and why?