Chrissy has two types of clients - the first type of clients are those that need to maintain high levels of protein intake, have intensive work-outs 4 days a week, and need to lower their body weight. The second type of clients are those that need to increase their weight along with their fitness levels for optimal outcome of their sessions with Chrissy. She realizes that the Nutritional Blend she created earlier would be sufficient for the first type of client, but the second type of clients require a different blend for their nutritional needs. Thus, Chrissy decides that she would create two different formulas using the same TypeA, Type B, and Type C protein powders, where Formula 1 would cater to the first type of client and Formula 2 would cater to the second type of client. Formula 1 contains 50 gm of protein, 40 gm of carbohydrates, and 30 gm of fat per serving whereas Formula 2 contains 20 gm of protein, carbohydrates, and fats each per serving. The cost of producing 1 lb of Formula 1 is $11.99 and the cost of producing each pound of Formula 2 is $9.52. Chrissy intends to sell Formula 1 for a price of $20 and Formula 2 for a price of $15 per pound. The following table shows that Chrissy has spent $995 in obtaining TypeA, Type B, and Type C protein powders at this time. Her calculations have shown that Formula 1 contains 20% of TypeA, 32% of Type B, and 49% of Type C powders, whereas Formula 2 contains 5% of TypeA, 31% of Type B, and 64% of Type C powders. Remember that the percentages also represent the proportion of each type of formula per lb. Help Chrissy determine how many pounds of Formula 1 and Formula 2 should she create from her ingredients tomaximize her profit using a linear programming model. (Remember Profit = Selling price per lb. - Cost per lb.)

Chrissy (from the earlier questions) has two types of clients - the first type of clients are those that need to maintain high levels of protein intake, have intensive work-outs 4 days a week, and need to lower their body weight. The second type of clients are those that need to increase their weight along with their fitness levels for optimal outcome of their sessions with Chrissy. She realizes that the Nutritional Blend she created earlier would be sufficient for the first type of client, but the second type of clients require a different blend for their nutritional needs. Thus, Chrissy decides that she would create two different formulas using the same Type A, Type B, and Type C protein powders, where Formula 1 would cater to the first type of client and Formula 2 would cater to the second type of client. Formula 1 contains 50 gm of protein, 40 gm of carbohydrates, and 30 gm of fat per serving whereas Formula 2 contains 20 gm of protein, carbohydrates, and fats each per serving. The cost of producing 1 1b of Formula 1 is $11.99 and the cost of producing each pound of Formula 2 is $9.52. Chrissy intends to sell Formula 1 for a price of $20 and Formula 2 for a price of $15 per pound. The following table shows that Chrissy has spent $995 in obtaining Type A, Type B, and Type C protein powders at this time. Her calculations have shown that Formula 1 contains 20% of Type A, 32% of Type B, and 49% of Type C powders, whereas Formula 2 contains 5% of Type A, 31% of Type B, and 64% of Type C powders. Remember that the percentages also represent the proportion of each type of formula per 1b. Help Chrissy determine how many pounds of Formula 1 and Formula 2 should she create from her ingredients to maximize her profit using a linear programming model. (Remember Profit = Selling price per 1b. - Cost per 1b.) Formula 1 Formula 2 Price/lb Purchased Lbs Amt. Spent Type A 0.20 0.05 $25.00 15 $375.00 Type B 0.32 0.31 $10.00 30 $300.00 Type C 0.49 0.64 $8.00 40 $320.00 Selling Price $20 $15 TOTAL Spent $995.00 Cost/1b $11.99 $9.52 Write out the Linear Program (equations) that Chrissy should use for maximizing her profit from both Protein Formulas. Fill in the following blanks: a. The Optimal Solution for Chrissy is to produce lbs of Formula 1 and lbs of Formula 2 to maxim ize her profits to $ (round to two decimal places) b. If Chrissy purchases an additional pound of Type A formula, her profits can increase by $ round o two decimal spaces)