Sphere foods company produces a candy called  "little Stars," a bag of dozen, individually wrapped, star-shaped candies made primarily from a blend chocolate, macadamia nuts, and a blend of heavy cream fillings. The candy is shipped in cases with 160 bags of candy per case. it has collected demand data ( i.e..., cases sold) from stores it supplies for the past four years, as shown in the accompanying table.

Year                 Demand ( cases)

1                      2706

2                       2968

3                       3180

4                        3350

Each case of candy weighs 120 Ibs. Each candy is made with 405 chocolates, 30% nuts and 30% heavy cream.

The company orders chocolate, nuts, and filling from its preferred suppliers by pound. 

the ordering cost for chocolate  is $5700 and the carrying cost is $ 0.45 per pound per year. The ordering cost for macadamia nuts is $6300, and the annual carrying cost is $ 0.63 per pound per year. The ordering cost for filling is $ 4500, and the annual average carrying cost is $0.55 per pound per year. ( 1 pound = 16 ounces)'

each of the suppliers  offers the candy manufacturer a Quantity-discount schedule for the ingredients as follows;

      Chocolate                               Macadamia Nuts                                                 Filling

cost           Quantity ( Ibs)            cost                 Quantity ( Ibs)                       cost                    Quantity ( Ibs)                 

$ 3.05        0-49,999                    $ 6.50               0-29,999                               $ 1.50                  0-39,999

2.9            50,000-99,999              6.25                30,000-69,999                        1.35                    40,000-79,999

2.75         100,000 +                      5.95                 70,000 +                                 1.25                    80,000 +

(a). Forecast demand for year 5 using the linear regression

( b). Calculate the total annual requirements for each ingredient from the annual demand forecast.

( c ). Determine the inventory order quantity for each of the three ingredients ordered from its  suppliers.

( d). Calculate the total inventory cost ( including purchase cost) for the year to meet the annual demand.