Golf Shafts, Inc. (GSI), produces graphite shafts for several manufacturers of golf clubs. Three GSI manufacturing facilities, one located in San Diego, one in Tampa, and the other in Boston have the capability to produce shafts in varying degrees of stiffness, ranging from regular models used primarily by average golfers to extra stiff models used primarily by low-handicap and professional golfers. GSI just received a contract for the production of 200,000 regular shafts and 175,000 stiff shafts. Because all plants are currently producing shafts for previous orders, neither plant has sufficient capacity by itself to fill the new order. The San Diego plant can produce up to a total of 170,000 shafts, the Tampa plant can produce up to a total of 100,000 shafts, and the Boston plant can produce up to a total of 105,000 shafts. Because of equipment differences at each of the plants and differing labor costs, the per-unit production costs vary as shown here:

San Diego Cost Tampa Cost Boston Cost

Regular shaft $5.25 $4.95 $5.05

Stiff shaft $5.45 $5.70 $5.32

a. How many regular shafts are to be produced in San Diego, Tampa and Boston plants respectively in order to minimize the cost?

b. How many shafts (regular+stiff) in total do San Diego, Tampa and Boston plants have to produce in order to minimize the cost?

c. What is the value of the objective function?

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\begin{array}{c|c|c|c} \;\ & \text{San Diego}&\text{Tampa}&\text{Boston}\\ \hline \text{regular}&5.25&4.95&5.05\\ \hline \text{stiff}&5.45&5.70&5.32\end{array}

x_{1}=\text{number of regular at San Diego}

x_{2}=\text{ number of stiff at San Diego}

x_{3}=\text{ number of regular at Tampa}

x_{4}=\text{ number of stiff at Tampa}

x_{5}=\text{ number of regular at Boston}

x_{6}=\text{ number of stiff at Boston}

Objective function is to minimize cost. Using the chart:

Min(Z)=5.25x_{1}+5.45x_{2}+4.95x_{3}+5.70x^{4}+5.0 5x^{5}+5.32x_{6}

Subject to the constraints:

x_{1}+x_{3}+x_{5}=200000

x_{2}+x_{4}+x_{6}=175000

x_{1}+x_{2}\leq 170000

x_{3}+x_{4}\leq 100000

x_{5}+x_{6}\leq 105000

x_{1},x_{2},x_{3},x_{4},x_{5},x_{6}\leq 0

Can you use Excel Solver to solve this? You can do it by hand using the Simplex or some other method, but that is too laborious.