Question 1166879: Its several months before Christmas - New Year’s holiday season. Wholesalers for Barako’s Distilled Spirits have been busy taking orders and will soon be making deliveries to retailers to stock their shelves for the holiday season. During the next 2 weeks, Barako’s must decide on the quantities of its two principal products to be bottled and shipped.
The firm’s vice-president of sales, Sheilla Valdez, has negotiated contracts for minimum shipments to the firm’s customers. She has also created this year an attractive promotion campaign to attract new customers. Valdez expects that, as a result of the advertising program, the company’s sales during the holiday season will come close to those of the firm’s chief rival, Don John, whose aromatic cognac has been the top choice of discriminating holiday revelers for the past decade.
The following table indicates the minimum amounts that Valdez has contracted to supply the firm’s wholesalers. It also shows the maximum amounts that she believes the firm can sell this season - provided, of course, that the bottling plant has sufficient amounts of the necessary ingredients. This table also indicates the profit margins on the two products: a relatively low-price blend, New Rhythm and a premium product - Crown Alternate.
table row cell P r o d u c t end cell cell M i n i m u m space G a l l o n s end cell cell M a x i m u m space G a l l o n s end cell cell P r o f i t space M a r g i n comma space left parenthesis P h P divided by G a l l o n right parenthesis end cell row cell N e w space R h y t h m space left parenthesis N R right parenthesis end cell cell 30 comma 000 end cell cell 80 comma 000 end cell cell 2.50 end cell row cell C r o w n space A l t e r n a t e space left parenthesis C A right parenthesis end cell cell 15 comma 000 end cell cell 40 comma 000 end cell cell 4.00 end cell end table
The two products are concoctions of Dr. M. dela Torre, research chemist at Barako’s, who is in charge of quality control. Besides a standard alcohol base, which is available in unlimited quantities, New Rhythm and Crown Alternate include a blend of two secret ingredients, which give the products their distinctive flavors and appeal. The amounts of these two ingredients (in percentage by volume) in the two products are as follows:table row cell P r o d u c t end cell cell P e r c e n t a g e space b y space V o l u m e space o f space S e c r e t space I n g r e d i e n t space A end cell cell P e r c e n t a g e space b y thin space V o l u m e space o f space S e c r e t space I n g r e d i e n t space X end cell row cell N e w space R h y t h m space left parenthesis N R right parenthesis end cell cell 2.0 end cell cell 3.0 end cell row cell C r o w n space A L t e r n a t e space left parenthesis C A right parenthesis end cell cell 1.0 end cell cell 5.0 end cell end table
The amount of the two ingredients that the company has available for blending during the production period are limited to 2,000 gallons of ingredient A and 2,500 gallons of ingredient X.
Answer by ikleyn(52765)   (Show Source):
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